







Quadratic Equations 
20170328 

From Natalie:
Hi Maths Central,
I am having trouble with quadratic equations. The question is:
Calculate the length 'l' of a rectangular pool by creating and solving a quadratic equation.
1. The rectangular pool is of equal area to a square pool, and a circular pool (5.70m^2).
2. The length of the rectangular pool must be 2m longer than the width 'w'.
Thank you so, so much for your help, Maths Central! Answered by Penny Nom. 





Solve 3x^219x14=0 for x 
20170315 

From nick: I'm an 8th grader and am quite confused with this equation:
3x^219x14=0
The answer is:
2/3 , 7
But I'm not sure how to solve for it. Answered by Penny Nom. 





Form the quadratic equation which has given roots 
20170116 

From Tharshini: Given a and B are the roots of the quadratic equation x^2+4x+7=0. Form the quadratic equation which has the roots
3a1 and 3B1 Answered by Penny Nom. 





Solve 2^2x + 3(2^x)  4 = 0 
20160427 

From Lloyd: Solve the equation 2^2x + 3(2^x)  4 = 0 Answered by Penny Nom. 





A quadratic equation with equal roots 
20160123 

From abdiwahid: X^2+2ax+4x+9a=0 is quadratic equation which has equal roots. Find the possible value of a? Answered by Penny Nom. 





Find the quadratic equation whose roots are 4 and 7 
20160103 

From sadiya: Find the quadratic equation whose roots are 4 and 7 Answered by Penny Nom. 





Fencing around a rectangular field 
20151111 

From Darlene: Question from Darlene, a parent:
A farmer has 10,000 meters of fencing to use to create a rectangular field. He
plans on using some of the fencing to divide the rectangular field into two
plots of land by constructing a fence inside the rectangle that is parallel to one
of the sides. Let X be the width of the rectangular field. Write an equation
to express the area of the field as a function of X. Find the value of X that
maximizes the area of the field. Answered by Penny Nom. 





A quadratic equation with known roots 
20151101 

From Awudu: Given the roots of the quadratic equation ax^2+5x+c=0 are 5 and 2/3,find the values of a,b and c. Answered by Penny Nom. 





2p^2+4p=16. How do i get p? 
20150922 

From Dohie: How do i solve this?
2p^2+4p=16. How do i get p?
Thanks Answered by Penny Nom. 





Two consecutive positive integers 
20150301 

From meha: Find two consecutive positive integers , sum of whose squares is 365. Answered by Penny Nom. 





Two quadratic equations 
20141120 

From rajesh: Sir,
I would like to discuss on question
Find the value of variable X and Y, equations are
X2+Y2+2XY=25
X2+Y22XY=1
Sir, my point is equation looks not so easy.My opinion is there many
(more than 4)value possible for both X and Y.
Kindly help me.
Waiting for your response.
regards,
rajesh Answered by Penny Nom. 





A quadratic function modelling the heightof a flea jump 
20141102 

From Hannah: A flea jumps from the ground to a height of 30 cm and travels 15 cm horizontally from where it started. Suppose the origin is located at the point from which the flea jumped. Determine a quadratic function in vertex form to model the height of
the flea compared to the horizontal distance travelled Answered by Penny Nom. 





Two quadratic polynomials 
20141028 

From khushboo: The zeroes of a quadratic polynomial x^2+ax+b are 'c' and 'd'
and the zeroes of a quadratic polynomial x^2+cx+d=0 are 'a' and 'b'.
find the numerical value of a+b+c+d where a, b, c and d are non zero integers. Answered by Penny Nom. 





A quarter mile row of trees 
20141009 

From junna: a farmer would like to plant trees on one side
of his lot which is 1/4 of a mile in a length
His friend advised him that if he would plant
the trees 5 feet farther apart,he would need 44
fewer trees.If the farmer would take the advice,
how many trees would he plant? Answered by Penny Nom. 





One zero to a quadratic expression 
20141006 

From Kevin: Find a value of n such that f(x) = 3^x2 + nx + 6 only has one zero, is this the only solution to the question? Answered by Penny Nom. 





A quadratic equation 
20140920 

From Najah: (E): (m2_1)x2 _ (m+3)x+4_m2=0
A) for what values of m is the equation (E) quadratic?
B) for what value of m is the real number 1 a root of (E) Answered by Penny Nom. 





The inverse of f(x) = x^2  x 
20140822 

From Tyler: Find the Inverse function of:
f(x) = x^2  x Answered by Robert Dawson. 





A quadratic equation given the roots 
20140423 

From Sarah: How do you find the quadratic formula when you're given just the roots ... X=3 X= 1/3
Thanks ! Answered by Robert Dawson. 





A quadratic equation 
20131127 

From corinanna: Hi,
How do you find a quadratic equation given the domain & range,
& or the yintercept? Answered by Penny Nom. 





Solve 0=2(x5)^2+4 
20131117 

From Leila: How do you find the solution to 0=2(x5)^2+4 Answered by Penny Nom. 





A quadratic with no real roots 
20130715 

From Pranav: If ax^2+bx5=0 has no real roots. Then d sign of 1) a+b5
2) (25a5b5)(4a+2b5) will be what ?? Answered by Penny Nom. 





The quadratic formula 
20130103 

From itsel: Find the discriminant ans use it to determine the use the quadratic formula to solve the equasion 2x^2+3x+2=0 Answered by Penny Nom. 





Two quadratic equations 
20121122 

From fahmie: graph and solve the intersection of the following equations:
x^2+y^2=4
x^2+2y=4 Answered by Penny Nom. 





A quadratic function 
20120608 

From Salehah: Hi there, i dont know how to do quadratic equations. So how do i do the question,
that says: xint 4 and 2, and yint of 4? and we are to maek a quadratic function with this information.
Please help!
Thank you very much!
Salehah Answered by Robert Dawson. 





Factoring a quadratic 
20120313 

From Makell: X^2 + 32x + 220 = 0 Answered by Penny Nom. 





Designing aluminum cans 
20120108 

From swathi: A company manufactures aluminum cans. one customer places an order for cans that must be 15 cm high, with a volume of 1200cm cube.
a) use the formula V= pie r squared h to determine the radius that the company should use to manufacture these cans
b) graph the function that corresponds to 0 = pie r squared h minus V to determine the radius. Answered by Penny Nom. 





A parabolic arch 
20120104 

From Swathi: A plan for an arch in the shape of a parabola is drawn on a grid with a scale of 1m per square.
The base of the arch is located at the points (0,0) and (15,0). The maximum height of the arch
is 18m.
a)Determine the quadratic function that models that arch
b)State the domain and range of the function Answered by Penny Nom. 





The graph of a quadratic function 
20111227 

From Thomas: sketch a quadratic function with zeros at 3 and 1 Answered by Penny Nom. 





Three consecutive numbers 
20111129 

From Michael: Find three consecutive numbers such that the second number squared
is equal to the first and third added together Answered by Penny Nom. 





Expanding the size of a table 
20111016 

From Ericka: You are working as a carpenter in an industrial Shop. A customer came to you and inquired about the size of the table which would be fitted in her room. She informed you that she had already a 1.5 x 1m table in her room but she wanted to maximize the space by adding the same amount to is length and width. She is planning to occupy a 3 square meter place on her room for her to work comfortably. She is requesting you a written recommendation before she asked to make a table. What amount should be added to both sides to maximize a 3 square meter area? Answered by Penny Nom. 





A picture with a frame 
20110819 

From Aniish: A picture 8inches by 12inches is placed in a frame of uniform width. If the area of the frame equals the area of the picture find the width of the frame? Answered by Penny Nom. 





(4x5)(3x+2)=0 
20110504 

From Corina: solve: (4x5)(3x+2)=0 Answered by Penny Nom. 





The radius of a cylinder 
20110427 

From Jazmin: Hi, I don't understand how to find the radius in a cylinder with only the surface area (143.7) and the height (0.8)? I know that the formula is 2pir2+2pirh, but I don't see how to isolate the r? I appreciate your help. Answered by Penny Nom. 





The quadratic with two given roots and a constant term 
20110419 

From Lindah: how do I food quadratic with two given roots and a constant term? Answered by Penny Nom. 





Solve x(x3) = 5 (x+4) 
20110419 

From Ashley: I have to solve using the quadratic formula. And my answer should be in simplest exact form. And I can't approximate.
I really need help to prepare for a test ....
x(x3) = 5 (x+4) Answered by Penny Nom. 





Throwing a football 
20110208 

From Janet: a football is thrown into the air from 2 meters high. After 1 second it is 6.9 meters high. After another second it is 2 meters high. How high is it after 1.02 seconds and .05 seconds? when will it reach 5.136 meters? I am not sure how to extract the numbers I need and what equations to use them in? Answered by Stephen La Rocque. 





Identify each polynomial by its degree and number of terms 
20110110 

From betty: Write in standard form and identify each polynomial by its degree and number of terms. How do you do this? Answered by Penny Nom. 





An algebraic equation with fractions 
20100910 

From leah: If 6/x  (x1)/2 = 4
then the LCD is 2x, right?
so you get 12/2x  (x2x)/2x = 8x/2x, right?
then what do you do with the 2x when you turn it into a quadratic equation? Answered by Penny Nom. 





The suspension cables of a bridge 
20100729 

From Mike: what is the formula for the suspension cables of a bridge.
The towers are 200 ft above the roadway
The towers are 3400 ft apart
The cable if at 8ft in the middle of the span Answered by Robert Dawson. 





The intersection of two graphs 
20100627 

From Austin: In depth explanation of how to find the intersection points of functions y=4t+300 and y=4.9(t5)^2+300 Answered by Stephen La Rocque. 





A quadratic equation with imaginary numbers 
20100603 

From Alissa: I am solving a quadratic equation and I got this far;
(x4+i)(x4i)=0
but how do I add the imaginary numbers
i know you multiply x by x and then add 4 + 4 but what do you do with the i's? Answered by Penny Nom. 





The product of two consecutive even integers 
20100511 

From Terry: The product of two consecutive even integers is 14 more than their sum. Find the integers. Answered by Penny Nom. 





Modelling an underpass 
20100511 

From Sue: An engineer at the Ministry of Transport is creating the plans for a new road. This road
will cross the path of a busy railway track so it will be necessary to built an underpass for this road.
This underpass will be in the shape of a parabolic arch.
The specifications include:
the road must be at least 10 m wide and it must have shoulders at least 2 m wide on either
side of the road.
there must be a clearance of 3 m over all areas of the road.
What quadratic equation could you use to model this bridge. Answered by Penny Nom. 





A quadratic equation 
20100503 

From Millie: (3x4)(5xplus2)=0 Answered by Penny Nom. 





A model for the population of a Canadian city 
20100407 

From jess: Let t^2 represent tsquared. The population of a Canadian City is modelled by: f(t) = 12t^2 + 800t + 40,000, where t is the time in years. When t= 0, the year is 2007.
a) According to the model, what will the population be in 2010?
B) In what year is the population predicted to be 300,000? Answered by Penny Nom. 





A quadratic equation 
20100315 

From rachelle: under certain condition, it is found that the cost of operating an automobile as a
function of speed is approximated by a quadratic equation. use the data shown
below to find the function. then use the function to determine the cost of operating
the automobile at 60mph.
speed
(in miles per hour) 
operating cost
per mile(in cents) 
10 
22 
20 
20 
50 
20 
Answered by Penny Nom. 





A piece of string 8 inches long is cut in two pieces 
20100202 

From Susan: If you have a piece of string 8 inches long and cut it in two pieces. Then take the pieces and forms
each into a square such that the area of each squares added together equals 2. How long are the
sides of the squares?
Susan Answered by Penny Nom. 





The discriminant 
20100117 

From Sonjonnia: What is the value of the discriminant?
16x^=16x4 Answered by Penny Nom. 





The minimum point of a quadratic 
20091231 

From rachel: y=0.0008x^20.384x
What is the minimum point of this equation? Answered by Penny Nom. 





Maximizing the area of a rectangle 
20091217 

From rachel: A rectangular field is to be enclosed by 400m of fence. What dimensions will give a maximum area? Answered by Penny Nom. 





Simplifying a quadratic expression 
20091207 

From Sabbie: Hi, I need help solving this equation for my physics homework,so I can solve the quadratic equations for x and y.
I've derived the following equations from the information provided in the question.
2a+3b = 4  1
2a^2 + 3b^2 = 62  2
a=2(3/2)b is substituted into equation 2.
so, i get
2 (2(3/2)b)^2 + 3b^2 = 62
this is where the problem begins. i cannot work through this to get to the correct quadratic equation
5b^28b36=0
I can't seem to be able to figure out where I keep going wrong. I would really appreciate it if you could give me a stepbystep breakdown of the workout.
thanks! Answered by Penny Nom. 





Factoring 
20091119 

From danyelle: 81x^2+36x+4
factoring i dont understand it at all Answered by Robert Dawson. 





The roots of a polynomial 
20091103 

From Jess: Find the value of a positive integer k such that f(x)=x^2  2kx + 55 has roots at k +3 and k  3. Answered by Penny Nom. 





Quadratic equations 
20090830 

From jovian: how can i find the quadratic equation of the roots 2/5 and 1/3? Answered by Stephen La Rocque. 





Factoring 
20090823 

From Bj: Solve for x: 5x^2  35x = 0 Answered by Stephen La Rocque. 





Factoring a quadratic 
20090616 

From Rebecca: solve the quadratic equation by factoring.
a) x(squared)+7x+10=0 Answered by Stephen La Rocque. 





4cos^2 (3x) + 3sin (3x) = 1 
20090505 

From Cheryl: Find all solutions of the following equation and show how to do this algebraically.
4cos^2 (3x) + 3sin (3x) = 1 Answered by Harley Weston. 





A quadratic equation with roots (4i) and (4+i) 
20090505 

From Kelly: find a quadratic equation with roots (4i) and (4+i) Answered by Harley Weston. 





Completing the square 
20090427 

From Daniel: I tried following an example of yours but I still couldn't figure it out.
Here is my question,
2x^2  6x + 1 = 0.
Any help would be greatly appreciated. Answered by Stephen La Rocque. 





cos2x = sinx 
20090419 

From stacey: solve the equation cos2x = sinx for 0 < x < 2 pi
giving the answer in terms of pi. Answered by Harley Weston. 





Winding paper after a break 
20090410 

From Olen: Question from Olen:
I work in a paper mill and have been handed the task to search for a formula to determine how much paper needs to be added to a parent roll to make up the difference at the winder. (Ex. The spool diameter at the reel is 18.25" we measure roughly 33.5" to make two 58" rolls in the winder. If the is a paper break and the roll diameter in the winder is 30" how much do I add to a single parent roll (22" roughly) to make one 58 " and the 28" needed at the winder. I would appreciate any help to complete this task. I would like to be able to build a chart that operators can refer to based on what is needed. Thank you. Answered by Harley Weston. 





Substitution in a quadratic 
20090309 

From Kieran: How could I work this out please
f(x)= 3xsquared  4x + 2
if f(2x) Answered by Penny Nom. 





Intercepts in a Quadratic Function 
20090222 

From Barb: I have a question I need help with please. What are the number of x and y intercepts that quadratic function can have and why?
Thanks. Answered by Janice Cotcher. 





Simultaneous equations with an xy term 
20090201 

From angelee: xy+5x2y10=0
2x+y=1 Answered by Penny Nom. 





ax^2 + bx + c = 0 has no real roots and.... 
20090126 

From Alberto: The equation ax^2 + bx + c = 0 has no real roots and a + b + c < 0 . Chose the right answer:
(A) c > 0
(B) c <= 0
(C) c = 0
(D) c >= 0
(E) c < 0
Explain the choice. Answered by Robert Dawson and Harley Weston. 





Gravity's Effect at a Distance 
20081206 

From ROHAN: AT WHAT HEIGHT FROM THE SURFACE OF EARTH,THE WEIGHT OF THE BODY BECOMES HALF? (RADIUS OF THE EARTH = 6400) Answered by Stephen La Rocque. 





What is so important about quadratics? 
20081129 

From zoe: what is so important about quadratics? Answered by Harley Weston. 





Quadratic equations arising from practical problems 
20081124 

From Lenval: Why do quadratic equations arising from practical problems often give physically impossible solutions such as negative distances, negative times or, say, a polygon with a negative number of sides? For example: "A river in flood carries a tree tsquared  23t metres downstream in t seconds. How long does it take for the tree to be carried 50 metres downstream?" This gives t=25 and t=2. Please explain the second 'solution', which is not physically possible. Answered by Chris Fisher and Victoria West. 





Factor 9x^2 + 6x + 4 
20081121 

From Jonah: how can i solve this by factoring: 9x^2 + 6x + 4 Answered by Harley Weston. 





A quadratic 
20081027 

From Giselle: 3x squared minus 2x equals 5 Answered by Penny Nom. 





Solving an Equation with a Square Root 
20081005 

From Jonathan: the square root of 3x+18 = x
3x+18 are within the square root Answered by Victoria West. 





cos^2x  3cosx = 1 
20080929 

From Danielle: cos2x  3cosx = 1 Answered by Penny Nom. 





Finding Traveling Time of a Projectile Given a Formula 
20080917 

From David: A juggler tosses a ballinto the air with a velocity of 40ft/sec from a height of 4 ft. Use s= 6t^2 + vot+so to find how long it takes for the ball to return to the height of 4 ft.
I was wondering how should i start this out, and can you give me a brief explanation on the formula they ask you to use? thx Answered by Janice Cotcher. 





The Width of a Mown Strip of Lawn 
20080915 

From Rimi: USE FACTORING, QUAD FORMULA, AND COMPLETE THE SQUARE!
Chris cuts half a rectangular lawn, 40m by 30m, by mowing strips
of equal width around the perimeter. Jonah cuts the small rectangle
left. How wide a strip does Chris cut so that they share the work equally? Answered by Harley J Weston. 





y^2+3yz8z4z=0 
20080817 

From Rae: y^2+3yz8z4z=0 Answered by Penny Nom. 





Two problems involving reciprocals 
20080810 

From Dee: I have a few questions that im have trouble working out...
1. One number is three times another number; if each is increased by 1 the sum of the reciprocals is 10/21. Find the numbers
2.A tank can be filled by 2 pipes together in 6 hours; if the larger pipe alone takes 5 hours less than the smaller to fill the tank, find the time in which each pipe alone would fill the tank Answered by Penny Nom. 





algebra 
20080731 

From Eric: Would you please solve & explain this equation to me: x^2+2x=x(x+2)?
Thank you Answered by Penny Nom & Stephen La Rocque. 





Width of a Garden Path 
20080730 

From Erin: A rectangular garden has dimensions of 18 feet by 13 feet. A gravel path of uniform width is to be built around the garden. How wide can the path be if there is enough gravel for 516 square feet? Answered by Janice Cotcher. 





Factoring a quadratic trinomial 
20080721 

From Jeff: c^2+4c+4
x^27x18 Answered by Penny Nom. 





A Falling Rock 
20080711 

From Rita: This question has 3 parts.
If a rock falls from a height of 20 meters on the planet Jupiter, its height H
(in meters) after x seconds is about H(x) = 20  13x^2
(a) What is the height of the rock when x = 1.2 seconds?
(b) When is the height of the rock 15 meters?
(c) When does the rock strike the ground?
Thank you Answered by Janice Cotcher. 





Sum and product of the roots of a quadratic 
20080703 

From Gautam: If a and b are the roots of x^2+px+1=0 and c and d are the roots of
x^2+qx+1=0
prove that
(ac)(bc)(a+d)(b+d)=q^2p^2
Regards
Gautam Answered by Harley Weston. 





3y^2  48 = 0 
20080623 

From marquis: 3y^2  48 = 0 Answered by Stephen La Rocque. 





A quadratic equation 
20080603 

From Drew: A solution of x^28x=17 is
4 or 4+I or 4 or 4+i Answered by Janice Cotcher. 





The area of a rectangle 
20080527 

From Becky: the area of a rectangular lot is represented by 6t^2+13t5. What are the length and the width of the rectangular lot? Answered by Harley Weston. 





Factor and solve s1^2  10s1  200 = 0 
20080429 

From KIM: please factor and solve s1^2  10s1  200 = 0 Answered by Stephen La Rocque and Penny Nom. 





Find the quadratic equation with roots at (3i) and its complex conjugate 
20080422 

From Tiffany: Find the quadratic equation with roots at (3i) and its complex conjugate. Answered by Penny Nom. 





A quadratic equation with odd coefficients 
20080415 

From Manashi: If p,q,r be any odd integers, then prove that the roots of the quadratic equation px^2+qx+r=0 can't be rational . Answered by Stephen La Rocque. 





A rectangle word problem 
20080410 

From Nick: A rectangle is twice as long as it is wide. If the length and width are both increased by 5cm, the resulting rectangle has an area of 50cm^2. Find the dimensions of the original. Answered by Penny Nom. 





The product of the roots 
20080319 

From Rebecca: Determine the product of the roots of the equation
(x1)(x2) + (x2)(x5)=0 Answered by Penny Nom. 





The sum and product of the roots of a quadratic 
20080316 

From Katelyn: Write the quadratic equation....
Sum of the roots = 16
Product of the roots = 80 Answered by Penny Nom. 





(x^2+x22)^4/3=16 
20080311 

From Ryan: (x^2+x22)^4/3=16
I keep on getting thrown off because of the fractional exponent I couldn't find an example like this one Answered by Stephen La Rocque. 





Completing the square 
20080311 

From Ryan: solve for x by completing the squares,
x^2+4x8=0 Answered by Stephen La Rocque. 





A complex quadratic 
20080218 

From Ash: z^2(6+2i)z+(8+6i)=0
Solve for Z Answered by Steve La Rocque and Penny Nom. 





Shooting an arrow over a wall 
20071211 

From Amy: The path of a large arrow fired from a non
torsion catapult can be modeled by y=0.0044x^2 + 1.68x, where x is the distance the
arrow travelled (in yards) and y is the height of the arrow (in yards). Given the height of
a castle wall, find the safest distance from the wall to launch an arrow over a 120 yardhigh wall. Answered by Victoria West and Stephen La Rocque. 





A quadratic function word problem 
20071112 

From liz: A kernal of popcorn contains water that expands when the kernal is heated,
causing it to pop. The equations below give the "popping volume"y(in cubic centimeters per gram)
of popcorn with moisture content x(as a percent of the popcorn's weight).
hot air popping: y = 0.761x^2 + 21.4x94.8
hot oil popping: y = 0.652x^2 + 17.7x 76.0
A) for hot air popping, what moisture content maximizes popping volume? What is the maximum volume?
B) For hot oil popping, what mositure content maximizes popping volume? What is the maximum volume?
C) the moisture content of popcorn tyipcally ranges from 8% to 18%. Graph the equations for hot air and hot oil popping on the interval 8 less then or equal to x and less then or equal to 18.
D) Based on the graphs from part(c), what general statement can you make about the volume of popcorn produced from hot air popping verus hot oil popping for any moisture content in the interval8 less then or equal to x and less then or equal to 18. Answered by Penny Nom. 





Four triangles in a square 
20071015 

From Kristina: A square with side lengths of 6 cm is divided into 3 right triangles and a larger isosceles triangle. If the three right triangles have equal area, find the exact area of the isosceles triangle. Answered by Stephen La Rocque. 





Inverses of Quadratic Functions 
20071011 

From Elliot: I'm a special education tchr trying to demonstrate how to find the inverse (using algebra) of quadratic functions. Any help would be greatly appreciated. Answered by Steve La Rocque and Harley Weston. 





Problems solved using quadratic equations 
20071007 

From Lisa: a. Two positive numbers differ by 5. Their product is 234. What are the two numbers?
b. The sum of two numbers is 12. Their product is 30. What are the two numbers?
c.Two numbers differ by 5. Their squares differ by 55. What are the two numbers?
d. The sum of two numbers is 15. Their product is 56. By forming an equation, find the two numbers. Answered by Penny Nom. 





Factoring a quadratic 
20070904 

From Arlene: Question from arlene, a student:
x^+2x24=0 Answered by Stephen la Rocque. 





Can you solve this by factoring? 10r^2  35r = 10 
20070812 

From Aranxa: how do u solve this equation by factoring:
10r^2  35r = 10 Answered by Stephen La Rocque. 





The domain and range of a quadratic function 
20070717 

From Linda: I have been trying to solve this problem but I'm unable to figure it out. How do I find the domain and range of
y=(x+1)^23? Please explain...thanks! Answered by Stephen La Rocque and Penny Nom. 





Values of k for which k(x^2+2x+3)  4x  2 is never negative 
20070629 

From claire: Find the range of values of k for which k(x^2+2x+3)  4x  2 is never negative. Answered by Harley Weston. 





The roots of (x  k)(13x) + 1 = 0 
20070628 

From Claire: Show that the roots of (x  k)(13x) + 1=0 are real and distinct for all real values of k. Hence, or otherwise, find the range of 9sin^2 r  6sin r + 13 Answered by Harley Weston. 





15 = 19.2 t (time)  4.9 t squared 
20070611 

From Nicole: 15 = 19.2 t (time)  4.9 t squared Answered by Penny Nom. 





Solving a quadratic equation using the Quadratic Formula 
20070605 

From Stuart: Solve the following quadratic equation:
3xsquared5x4=0 Answered by Stephen La Rocque. 





Using FOIL for (2x  6)^2 
20070518 

From TONI: I am having a problem finding examples of how to solve (2x6)^2. Answered by Stephen La Rocque. 





Interval of the domain 
20070513 

From Gale: What does the term interval of the domain mean? Answered by Penny Nom and Stephen La Rocque. 





A sketch of a quadratic equation 
20070414 

From Fee: A ball is thrown upward from the roof of a 25m building. The ball reaches a height of 45m above the ground after 2s and hits the ground 5s after being thrown.
Use the fact that the realtion between the height of the projectile and time is quadratic to draw an accurate graph of the relation on graph paper. Answered by Penny Nom. 





A quadratic function 
20070412 

From sveta: determine the quadratic function
f(x)=ax^2+bx+c,such that f(x)+2x+8=f(x+1) , and f(1)=12 Answered by Stephen La Rocque. 





Intersection of a line and a circle 
20070412 

From gaby: The sum of two numbers is 9. The sum of the squares of the two numbers is 41. Find the numbers. Answered by Steve La Rocque and Melanie Tyrer. 





A quadratic problem 
20070412 

From Chin: The quadratic equation y = (xp)^2 + q cuts the y axis at y = 10. The straight line
y = 6 is a tangent to the curve. Find the values of p and q? Answered by Stephen La Rocque. 





Solving QuadraticLiner Equations algebraically 
20070412 

From Hector: Solving QuadraticLinear Equations algebraically.
y=x^24x+3
y=x1 Answered by Stephen La Rocque. 





Kicking a field goal 
20070313 

From san: A football player attempts a field goal by kicking the football. The ball follows
the path modelled by the equation h= 4.9^2+10t+3, where h is the height of the
ball above the ground in metres, and t is the time since the ball was kicked
in seconds.
*the ball must clear the uprights for the field goal to count. The uprights are approximately
5 m high. How long does the ball stay above 5 m in height? Answered by Penny Nom. 





Maximize revenue 
20070308 

From San: A movie theatre sells tickets for $8.50 each. The manager is considering raising the prices but knows that for every 50 cents the price is raised, 20 fewer people go to the movies. The equation R= 40c^2+84c describes the relationship between the cost of the tickets, c dollars, and the amount of revenue, R dollars, that the theatre makes. What price should the theatre charge to maximize revenue? This question comes from my gr.11 corresponding study homework and I not yet solve it. Please help! Thank you, I will appreciate your help. Answered by Stephen La Rocque. 





Finding the xintercept 
20070302 

From Ash: Y = 1/100X^2 =27/10X +0 = 0 THE Y INTERCEPT IS 50 HOW DO I FIND THE X INTERCEPT Answered by Gabriel Potter. 





Fencing a field 
20070201 

From Carol: "The area of a rectangular field is 1200m^2. Two parallel sides are fenced with aluminum at $20/m. The remaining two sides are fenced with steel at $10/m. The total cost of the fencing is $2200." What is the length of each side fenced with aluminum and steel? Answered by Stephen La Rocque. 





y = x^2  2 
20070108 

From Mike: Graph the quadratic equation: y=Xsq2 Answered by Penny Nom. 





The area of a triangle 
20061229 

From Paula: The area of a triangle is 24cm². Its height is 2cm more than its base. Determine the base and the height. Answered by Penny Nom. 





A quuadratic equation 
20061222 

From Harold: L=3w4 A=96Square I used the quadratic equation to solve and my answer is still wrong
I convert the square of 1168 to decimal.
here is where i start (3w4) x w=96
could you give me an example Answered by Stephen La Rocque. 





The roots of a quadratic equation 
20061116 

From Lana: If p and q are the roots of 2X^2 +3X+7=0, compute pq^3+qp^3. thanks for your help. Answered by Penny Nom. 





3x squared + 5x 2=0 
20061114 

From Stacey: my son has a problem I am trying to figure out neg 3x squared + 5x 2=0 Answered by Stephen La Rocque. 





Is this unsolvable? 
20060919 

From Al: Is this unsolvable???
2xy + 3x^2  3y + y^3 = 4x + 3 where y=3. Answered by Penny Nom and Claude Tardif. 





How do i factor x^3  6x^2 + 8x 
20060910 

From Lauren:
how do i factor
x^{3}  6x^{2} + 8x
Answered by Stephen La Rocque. 





Quadratics and quintics 
20060718 

From Lynne: What is wrong with this statement? "The quintic is one step up from the dread quadratic equation." (Newsweek, Dec. 19, 2005) Answered by Stephen La Rocque. 





The perimeter of a regular octagon 
20060420 

From Martin: I would like to make an octagon out of 2x4 lumber. I know that the lumber needs to be cut at 67.5 degree angles, but how do I determine the length of each piece if I want to make, say, a 2.5 ft diameter octagon? Answered by Stephen La Rocque. 





The quadratic formula 
20060303 

From Miriam: Please show work and indicate "answer", using the quadratic formula 
(x+2) (2x+3) = 6 Answered by penny Nom. 





6y^10 + 19y^5 + 14 
20060302 

From Bahija: Factor 6y^{10} + 19y^{5 }+ 14 Answered by Penny Nom. 





Solve for x 
20060205 

From Minti: how can you solve for x?
f(x) = 1/4pi(x²) =10x x²(4pi)/8 Answered by Penny Nom. 





Quadratic Equations & Given Roots 
20051111 

From Lindsey:
I need to find the quadratic equation in the form:
f(x)=a(x^{2}  (b/a)x + (c/a))
The vertex is (1, 7), the roots are (4, ?)
I need to find the other root but I don't know where to begin. My answer key says the other root is (2). How is this possible?
Answered by Penny Nom. 





How do you solve 3x^2 + x  2 = 0 
20050915 

From Lizzy: How do you solve 3x2 + x  2 = 0 Answered by Penny Nom. 





A quadratic 
20050906 

From Ginger: I took a pre alg test today. There was a question on it that I am not sure and is bothering me. Can you tell me the answer?
x square + 13 + 14
Factor this Answered by Penny Nom. 





x = (y^2  b^2)/2b 
20050904 

From Bob: while looking at x=(y^{2}b^{2})/2b on a table I was preparing for a graph, I saw that there is a point where x and y get closer to each other's value. By trial and error I tried to find the point where x=y. I saw a number which looked familiar and I realized it was the square root of 2. and so, if y=b(1+square root of 2) then x=b(1+square root of 2) also, or as x=y.
My question is: How can this result x=y when y=b(1+square root of 2) be algebraically derived from the equation x=(y^{2}b^{2})/2b without pre knowing it is so? Answered by Penny Nom. 





Discriminant 
20050620 

From A student: If a quadratic has real root, its discriminant b24ac>=0 Is there any similar condition or method by which you can find whether roots of a cubic equation are real or not? Answered by Chris Fisher. 





16x^2+20x12x15 
20050503 

From Tanya: how they got (4x+5)(4x5) from
16x^{2}+20x12x15=4x(4x+5)3(4x+5)=(4x+5)(4x5) Answered by Penny Nom. 





A quadratic equation 
20050427 

From Chris: Solve using the quadratic formula
9x² + 9x  5 = 0
I don't get the same answer as in the text book which is
3+/ ^{√29}/_{36}
Hope you can help....
Answered by Penny Nom. 





A quadratic equation 
20050209 

From Jess: 6x+8=x2 Answered by Claude Tardif. 





Solve for x 
20050202 

From Christie: Solve for x
.387 = (.40  .265x)/(sqrt(1x2)) Answered by Penny Nom. 





cos 2x = sin x 
20050122 

From Kris: solve the equation
cos 2x = sin x for 0<= x < 360 Answered by Penny Nom. 





Quadratics 
20050105 

From Usman: Hi, in my Grade 11 Functions math class we have been assigned the task of finding jobs and careers related to quadratics, I have done many searches but have been unsuccessful, then I saw your website and emailed. I also have to use an example of a math problem that the job uses, then solve it, this will all compile on bristol board for a presentation. I would greatly appreciate it if you could send me some links and references of sources that refer to this subject. Answered by Harley Weston. 





An elliptical table 
20050103 

From Roger: Want to make an elliptical table, say the long (major) axis is 4 feet, and the short (minor) axis is 3 feet. I can construct this figure, but I'm trying to figure out what the exact dimension of a rectangle within this ellipse will be if I make the table a drop leaf type where the drop dimensions are equal for each end of both the long and short axes. Intuitively, it looks like there is one and only one solution. Answered by Penny Nom. 





Solving quadratics 
20041120 

From Aaron: Can you solve the following equation (quote the value of x,y and t to 3 sig figs)
((i have changed figures so that i can work through my own example))
x^{2} + x  6 = 0
5y^{2} +19y = 3
10cos2 t + 3cos t = 4 Answered by Penny Nom. 





Factoring 
20041109 

From Rise: Q1: a^{2} + 5a + 6
I didn't really understand the purpose of the teacher's steps, but was able to get my daughter to find factors of 6 and then add them together to find which resulted in the sum of 5.
Unfortunately, this problemsolving technique did not help us to solve for the more complex problems as follows:
Q2: 9a^{3}  24a^{2} + 12a Answered by Penny Nom. 





Factoring 
20040728 

From Nicole: Can 4x2 + 19x + 12 be factored? i have tried but i cannot figure it out. Is there a way to find out if it cannot be factored before i try to work out the problem? Answered by Penny Nom. 





x^2 = x + 2 
20040726 

From A parent: x2 = x+2
My daughter came home with this equation today and although I know the answer is x=2, i have no way of proving it by showing any working out. Answered by Penny Nom. 





Solving some quadratic equations 
20040715 

From A student: Could you please solve the following for x
x^{2}+6=5x
x^{2}+16=8x
2x+21=3x^{2} Answered by Penny Nom. 





A tangent to a quadratic 
20040604 

From Jem: I have a question on the tangent to a quadratic curve.
Say I have a curve y = ax^{2} + bx + c. The gradient, using the derivative of y, at any point x on the curve is: 2ax + b right? Then, for the tangent that cuts the curve at a point x, the equation of the tangent can be: y1 = (2ax + b)x1 + d.
My question is, how is the point d of this tangent determined? It is the point on the yaxis where the tangent cuts isn't it? Is there a formula for it? Answered by Penny Nom. 





x^2/3  7 x^1/3 + 12 = 0 
20040405 

From Jackie: I am having trouble solving this question for x:
1.) x^2/3  7 x^1/3 + 12 = 0 Answered by Penny Nom. 





A quadratic word problem 
20040204 

From Carl: A walkway of uniform has 72m2 and surrounds a swimming pool that is 8m wide and 10m long. Find the width of the walkway. Answered by Penny Nom. 





x^2  12x = 8 
20040124 

From Sherre: x^{2}  12x = 8 Answered by Penny Nom. 





The product of the page numbers 
20031107 

From Morgan and Mom: You open a book and the product of the page numbers is 12,656. What are your page numbers? Answered by Penny Nom. 





The quadratic formula 
20030831 

From Alex: I am using Houghton Mifflin's Precalculus with Limits book, 2nd edition. However, the first chapter encompasses Algebra review, and I am stuck on a problem. All that's required is to solve the following and verify using a calculator: 3y2+6y+2=0 I have solved the problem using the quadratic formula, but from what I remember, the quadratic formula is used in the case of equations following the AX2+BX+C=0 pattern. As the problem I am attempting uses a yvariable, can I still use the quadratic formula? Since I am not sure what route to take in solving this problem, I am hoping you can assist me. Answered by Harley Weston. 





x6square root of x +8=0 
20030510 

From Elizabeth: x6square root of x +8=0 Answered by Penny Nom. 





Two intersecting graphs 
20030423 

From Patty:
a) graph the equation x^{2}  y  4 = 0
x^{2} + y^{2} = 9 on the same set of coordinate axes. I did not have a problem with this. The problem is part (b) of the question ask: Find all solutions of the system in part (a) algebraically. Express answers in decimal form, accurate to two decimal places. Answered by Penny Nom. 





Quadratic word problems 
20030330 

From A student: Question: i think i know the basics of how to solve direct quadratic equations,but how do i go about solving those word problems? i have tried them times and again, but nothing seems to work at all!they are driving me crazy! pls help!:):):):):)  bob & nick earned $1260 each. bob's hourly wage is $3 more than nick's hourly wage. he worked 2h less compared to nick. find the number of hours nick worked.
 there are 2 tanks in henry's house. in tank A, the fish are all goldfish. they are bought at a total cost of $259. in tank B, there are only guppies. the guppies were bought at a cost of $1.20 each. a day later,henry bought 3 more goldfish and put them into tank A. the number of guppies in tank B is now twice the number of goldfish in tank A.the total cost of all the fish that henry has presently,i.e. goldfish & guppies, is $355.30. given that the cost of each goldfish is the same,
a)find the initial number of goldfish in tank A b)find the total cost of all the guppies.  a particular disc can be made to rotate at 2 different speeds. if it is made to rotate slower by 135 revolutions per hour, it wld require an additional 2.7 hour to make 315 revolutions. find the higher speed at which it can operate.
Answered by Penny Nom. 





Why quadratic? 
20030121 

From Dan: Why are equations of the form aX^{2} + bX + c =0 call quadratic? The quad indicates 4 but the power is 2. Answered by Penny Nom. 





The intersection of conics 
20021219 

From Glenda: We are studying systems of equations where two conic sections are the two equations that we are solving simultaneously. We were studying the number of solutions that are possible if you have an ellipse and a parabola. We all agree that there can be none, one, two, three or four solutions. The question that the students had for me was whether or not a portion of an ellipse and a parabola can overlap and thereby allow an infinite number of solutions. What should I tell them? Answered by Chris Fisher and Harley Weston. 





Quadratic equations 
20021210 

From Katie: just bugging the hell outta me and I cannot figure it out for the life of me.
1)x2x1 =0 Find both roots. You must simplify both of your roots. This equation requires the use of the Quadratic Formula. I have tried everything for this and I am still either getting the wrong answers, and end up getting really frustrated. If you could find the answers and tell me how you did it I would greatly appreciate it! Then the second problem is
2) The square of a certain negative number is equal to 70 decreased by 3 times the number. Find the answer! On this one I set it up but still came out with the wrong answer. So if you could help me on this one I would greatly appreciate it! Answered by Penny Nom. 





A complex quadratic 
20021006 

From Michael: I would like to know, how to solve this Complex number: quadratic equation. ix^{ 2} + x i = 0 Answered by Harley Weston. 





The quadratic formula 
20020911 

From Kathleen: im having a problem trying to understand quadratic formulas can u please help me i have problems like 3x^{2}  4x  11 = 0 how do i work out that problem? i have the formula written down but it doesnt seem to register for me. Answered by Penny Nom. 





Factor 12x^2  20x  8 
20020430 

From Crystal: Factor Completely: 12x^{2}  20x  8 Answered by Penny Nom. 





A rightangled triangle 
20011213 

From Pamela, Jeff, Kayleigh and Jacob: A rightangled triangle has one side that is 8 cm shorter that the hypotenuse. The other side is 1 cm shorter than the hypotenuse. Find the length of the sides. Answered by Penny nom. 





Solving x^23x+5=0 
20011130 

From Katy: How do you find the solution to x^{2}3x+5=0? Answered by Penny Nom. 





Why quadratic for a second degree equation? 
20011020 

From Jana: Why do we use the word quadratic to describe second degree equations? Answered by Penny Nom. 





Quadratics 
20010516 

From John: I am in the final stages of a math project and I need to interview an expert for the last part. Please try to answer at least a few of these questions.  How do you use quadratic equations in your everyday life?
 Do you find being a math expert very helpful in life?
 Is the quadratic equation useful to you?
 Why did you decide to become a math expert?
 What do you think is the most important function of the quadratic equation?
Answered by Harley Weston. 





25 y^2 + 20 y z  4 z^2 
20010515 

From Kimmy: i don't know how to factor the trinomial 25y^{2} + 20yz  4z^{2}. I can get it, but i get messed up on getting the minus 4 at the end. all i get is a plus 4. Can it even be factored. Answered by Penny Nom. 





A quadratic function 
20010510 

From A parent: A quadratic function is given by f:xax^{2}+b
If the two points A(2, 2) and B (0, 8) are on the graph of the function, then find a and b. Answered by Penny Nom. 





Solving an equation 
20010327 

From Jennifer: How would I solve this equation? 1.6 = 2x/(.1x)  the equation in parenthesises is raised to the second power. I know you take the square root of both sides, but there is where I get lost. Answered by Leeanne Boehm. 





Quadratic equations 
20010311 

From Philip: I am a student in the UK and i am in secondary school and i am doing my GCSE next year. here are my questions: solve the following equations correct to 2 decimal each time. [1] 2xsquared + 5x = 1 [2] 3xsquared(2x+1)=1 [3] xsquared + 7x + 2 = 2x + 4 [4] 5xsquared  3x = xsquared + 4 Answered by Penny Nom. 





The solutions of a quadratic 
20010130 

From A student:
 Show that the product of the solutions of ax^{2} + bx + c = 0 is c/a.
 For each equation under the given condition, (a) find k and
(b) find the other solution. kx^{2}  2x + k = 0; one solution is 3 Answered by Penny Nom. 





Completing the square 
20010112 

From Jacky Lam: A friend told me that completing square not only can find the vertex but also the roots of a quadratic equation. Is it possible? How? Can you show me how to find the roots of the following equation using completing the square? 8x^{2} + 8x + 4 Answered by Penny Nom. 





A problem with a quadratic 
20000809 

From David Xiao: Find the value of a such that 4x^{2} + 4(a2)x  8a^{2} + 14a + 31 = 0 has real roots whose sum of squares is minimum. Answered by Harley Weston. 





Finding a Quadratic Equation given the roots 
20000416 

From A secondary student: How do I find the equation for the quadratic with roots at 2i and its complex conjugate? Answered by Harley Weston. 





Quadratics 
20000127 

From Lori:
Hi my name is Lori. I'm a student, in the 11th grade.I have a problem in quadratic functions. I don't know how to get the numbers into the problem and then how to do the problem. here is one problem the rest are sort of similar to it... y=2x squared. If I were to find out how to get the (x,y) answers then I could graph it but as I said I can't find the numbers to go into the problem. Also in the equation g: x arrow to y = x + 4..... how would you know weather it is or isn't a quadratic equation???? Answered by Penny Nom. 





Quadratic 
20000126 

From Karen Johnson: What is the reasoning behind the title quadratic equation? Answered by Penny Nom. 





Complex Roots 
20000124 

From Jess Rutherford: How do I find the value of k when 5x^{2} + k = 3x and has complex roots ? Answered by Penny Nom. 





Derive the quadratic equation 
20000101 

From Thuy: My teacher asked us this question in which i can't understand when she asked to derive the quadratic equation. What does this mean? Answered by Penny Nom. 





Two conics 
19991207 

From Quinn: I know the formula to find the axis of symmetry of a conic section (I'm not sure what shape  circle for the first one??) is (D/2A,E/2C) but I obviously don't get how to calculate it, because when I check the answer it's wrong, but I'm so close!! For the following equations my teacher suggested to "divide the x term coefficient, D, by the x squared term coefficient before...do the same for y." 2x^{2}+2y^{2}8x+12y+16=0 . . . Answered by Penny Nom. 





Critical numbers 
19991117 

From Sarah: My question is this: If f(x)=2x^{3}+4x^{2}9x+8 and the derivative is f'(x)=6x^{2}+8x9, how do I find the critical points if f'(x) is not factorable?? Answered by Penny Nom. 





Two Quadratics 
19991008 

From Jason On: Solve the following equations,expressing solutions in the form p + iq.  sqr(x) + 2x  1 = 0,
 sqr(x) + 2x  3 = 0.
Answered by Harley Weston. 





A ladder problem 
19990422 

From Michael Blade: There is a cube box 3feet x 3feet x 3ft resting against a vertical wall on level ground. Resting against the outside corner of the box is a ladder 10 feet tall, this ladder is of course resting on the ground but also against the outside corner of the box and rests on the wall. The question the ladder is divided into two unequal section bounded by the box to the ground and the box to the wall. what are those dimensions? Answered by Penny Nom. 





Quadratic equations 
19990331 

From Ken Niebergall: #1 a^{2}  10a = 2a  36 #2 t(t  5) = 5 (t  5) #3. (x + 4)(x  3) = 8 Thanks. Answered by Jack LeSage and Penny Nom. 





A word problem 
19990325 

From Anna Gariss: A second number is 4 less than a first number. The product of the second number and 3 more than the first number is 18. Find the pair of numbers. Answered by Jack LeSage and Penny Nom. 





An airplane problem 
19990308 

From B.M.R.: A plane left New York and headed East to its destination 3600 miles away across the Atlantic. On the way back its speed was boosted by a 50 mph tail wind and it arrived an hour early. What was its normal speed? Answered by Jack LeSage. 





Enlarging a Rink 
19990306 

From Jennifer Rudd: I've been having difficulty with this one question involving area. The level of the question is Grade 11/12. Here it is! A rink is 40 m long by 20 m wide. There are plans to enlarge it by 700m^{2} by adding a strip at one end and a strip of the same width along one side. Find the width of the strip. (Let the width of the strip by x meters.) Answered by Jack LeSage. 





The Quadratic Formula 
19990122 

From Eric Morgan: Hi my name is Eric Morgan and I m in 8th Grade honors math (middle) and I'd like to know how to prove the quadratic formula bħsqrt of b(a)(c)over 2(a) Answered by Penny Nom. 





Complex numbers and the quadratic formula 
19981225 

From Richard Peter: My age is 16, and my name is Richard. My question relates to the topic complex numbers & the quadratic formula. I would like to know how to solve quadratic equations in which the discriminant is less than 0 (i.e. we get two complex solutions to the quadratic) 3x^{2}+2x+5 = 0 and how mathematicians like euler contributed to this field. If it would be possible I would also like to know how this type of quadratic equations can be graphed? Answered by Harley Weston. 





Solving Quadratics 
19980716 

From Fred Goodrich: I need a step by step lesson on solving quadratic equations. Thank you, Answered by Penny Nom. 





Quadratic Graphs 
19980113 

From Simon Batten: How does varying the values a,b and c affect the graph of y=ax^{2} + bx + c? Answered by Harley Weston. 





Find the Numbers. 
19971228 

From Sandy C: The sum of the squares of two numbers is 53. Twice the greater, minus the lesser is 11. Find the numbers. Answered by Penny Nom. 





Polynomials 
19971007 

From Sheryl and Jeff: I'm a math teacher in Jerusalem, Israel. I'm teaching about graphing polynomial functions in a precalc class. A student asked me what they're good for. I couldn't give her a good example. Do you have one. Thanks. Answered by Penny Nom. 





Why QUADratic? 
19970319 

From Paula Miller: A student today asked me why a quadratic, with highest power of degree 2, was called a QUADratic. We're awaiting the answer with baited breath! :) Answered by Chris Fisher and Walter Whiteley. 





Deriving the Quadratic Formula 
19970204 

From James: How do you derive the quadratic formula? I know what it is, but the textbook doesn't say how to derive it. Answered by Penny Nom. 

