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Quandaries & Queries
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From Em:
One root of the equation 2x^2 + bx - 24 = 0 is -8. What are the possible values of b and the other root?
A line cuts a curve 2018-11-11
From roxanne:
Hello, i need to ask a question, do you mind explaining and writing the formula of how to solve equations such as "find the set values of k for which the line y-2x-5 cuts the curve y=x^2 +kx+11" please
The price of eggs rises 10 cents per dozen 2018-11-10
Hi! I'm currently struggling with a word problem that says: "If the price of eggs rises 10 cents per dozen, one will be able to get 2 dozen fewer eggs with \$6.00 than was possible at the lower price. What is the lower price? We are working on completing the square and all of the problems I've done so far in this chapter require using that method. If possible and needed, could you explain how to set up the equation? Thank you so much! I appreciate all your help!!
From Billy:
I need help factoring the following question: 4x(squared) -10x +16.
The intersection of a curve and a line 2018-03-08
From lola:
find the set of values of constant C for which the line y=x+c intersects the curve y=2 square root x at, at two distinct points
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!

Solve 3x^2-19x-14=0 for x 2017-03-15
From nick:
I'm an 8th grader and am quite confused with this equation: 3x^2-19x-14=0

-2/3 , 7

But I'm not sure how to solve for it.

Form the quadratic equation which has given roots 2017-01-16
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 3a-1 and 3B-1
Solve 2^2x + 3(2^x) - 4 = 0 2016-04-27
From Lloyd:
Solve the equation 2^2x + 3(2^x) - 4 = 0
A quadratic equation with equal roots 2016-01-23
From abdiwahid:
X^2+2ax+4x+9a=0 is quadratic equation which has equal roots. Find the possible value of a?
Find the quadratic equation whose roots are -4 and 7 2016-01-03
Find the quadratic equation whose roots are -4 and 7
Fencing around a rectangular field 2015-11-11
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.
A quadratic equation with known roots 2015-11-01
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.
2p^2+4p=16. How do i get p? 2015-09-22
From Dohie:
How do i solve this?

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

Thanks

Two consecutive positive integers 2015-03-01
From meha:
Find two consecutive positive integers , sum of whose squares is 365.
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+Y2-2XY=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.
regards,
rajesh

A quadratic function modelling the heightof a flea jump 2014-11-02
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
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.
A quarter mile row of trees 2014-10-09
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?
One zero to a quadratic expression 2014-10-06
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?
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)

The inverse of f(x) = x^2 - x 2014-08-22
From Tyler:
Find the Inverse function of:
f(x) = x^2 - x

A quadratic equation given the roots 2014-04-23
From Sarah:
How do you find the quadratic formula when you're given just the roots ... X=-3 X= 1/3 Thanks !
From corinanna:
Hi,
How do you find a quadratic equation given the domain & range, & or the y-intercept?

Solve 0=-2(x-5)^2+4 2013-11-17
From Leila:
How do you find the solution to 0=-2(x-5)^2+4
A quadratic with no real roots 2013-07-15
From Pranav:
If ax^2+bx-5=0 has no real roots. Then d sign of 1) a+b-5 2) (25a-5b-5)(4a+2b-5) will be what ??
From itsel:
Find the discriminant ans use it to determine the use the quadratic formula to solve the equasion -2x^2+3x+2=0
From fahmie:
graph and solve the intersection of the following equations:
x^2+y^2=4
x^2+2y=4

From Salehah:
Hi there, i dont know how to do quadratic equations. So how do i do the question, that says: x-int -4 and 2, and y-int of 4? and we are to maek a quadratic function with this information.

Thank you very much!
Salehah

From Makell:
X^2 + 32x + 220 = 0
Designing aluminum cans 2012-01-08
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.

A parabolic arch 2012-01-04
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

The graph of a quadratic function 2011-12-27
From Thomas:
sketch a quadratic function with zeros at -3 and 1
Three consecutive numbers 2011-11-29
From Michael:
Find three consecutive numbers such that the second number squared is equal to the first and third added together
Expanding the size of a table 2011-10-16
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?
A picture with a frame 2011-08-19
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?
(4x-5)(3x+2)=0 2011-05-04
From Corina:
solve: (4x-5)(3x+2)=0
The radius of a cylinder 2011-04-27
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.
The quadratic with two given roots and a constant term 2011-04-19
From Lindah:
how do I food quadratic with two given roots and a constant term?
Solve x(x-3) = 5 (x+4) 2011-04-19
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(x-3) = 5 (x+4)

Throwing a football 2011-02-08
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?
Identify each polynomial by its degree and number of terms 2011-01-10
From betty:
Write in standard form and identify each polynomial by its degree and number of terms. How do you do this?
An algebraic equation with fractions 2010-09-10
From leah:
If 6/x - (x-1)/2 = 4 then the LCD is 2x, right? so you get 12/2x - (x2-x)/2x = 8x/2x, right? then what do you do with the 2x when you turn it into a quadratic equation?
The suspension cables of a bridge 2010-07-29
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
The intersection of two graphs 2010-06-27
From Austin:
In depth explanation of how to find the intersection points of functions y=-4t+300 and y=-4.9(t-5)^2+300
A quadratic equation with imaginary numbers 2010-06-03
From Alissa:
I am solving a quadratic equation and I got this far;
(x-4+i)(x-4-i)=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?

The product of two consecutive even integers 2010-05-11
From Terry:
The product of two consecutive even integers is 14 more than their sum. Find the integers.
Modelling an underpass 2010-05-11
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.

From Millie:
(3x-4)(5xplus2)=0
A model for the population of a Canadian city 2010-04-07
From jess:
Let t^2 represent t-squared. 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?

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

A piece of string 8 inches long is cut in two pieces 2010-02-02
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

The discriminant 2010-01-17
From Sonjonnia:
What is the value of the discriminant?
16x^=16x-4

The minimum point of a quadratic 2009-12-31
From rachel:
y=0.0008x^2-0.384x
What is the minimum point of this equation?

Maximizing the area of a rectangle 2009-12-17
From rachel:
A rectangular field is to be enclosed by 400m of fence. What dimensions will give a maximum area?
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^2-8b-36=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 step-by-step breakdown of the workout.

thanks!

Factoring 2009-11-19
From danyelle:
81x^2+36x+4

factoring i dont understand it at all

The roots of a polynomial 2009-11-03
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.
From jovian:
how can i find the quadratic equation of the roots 2/5 and -1/3?
Factoring 2009-08-23
From Bj:
Solve for x: 5x^2 - 35x = 0
From Rebecca:
solve the quadratic equation by factoring.
a) x(squared)+7x+10=0

4cos^2 (3x) + 3sin (3x) = 1 2009-05-05
From Cheryl:
Find all solutions of the following equation and show how to do this algebraically. 4cos^2 (3x) + 3sin (3x) = 1
A quadratic equation with roots (4-i) and (4+i) 2009-05-05
From Kelly:
find a quadratic equation with roots (4-i) and (4+i)
Completing the square 2009-04-27
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.

cos2x = sinx 2009-04-19
From stacey:
solve the equation cos2x = sinx for 0 < x < 2 pi giving the answer in terms of pi.
Winding paper after a break 2009-04-10
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.

From Kieran:
How could I work this out please

f(x)= 3xsquared - 4x + 2

if f(2x)

Intercepts in a Quadratic Function 2009-02-22
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.
Simultaneous equations with an xy term 2009-02-01
From angelee:
xy+5x-2y-10=0 2x+y=1
ax^2 + bx + c = 0 has no real roots and.... 2009-01-26
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 2008-12-06
From ROHAN:
AT WHAT HEIGHT FROM THE SURFACE OF EARTH,THE WEIGHT OF THE BODY BECOMES HALF? (RADIUS OF THE EARTH = 6400)
From zoe:
Quadratic equations arising from practical problems 2008-11-24
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 t-squared - 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 2008-11-21
From Jonah:
how can i solve this by factoring: 9x^2 + 6x + 4
From Giselle:
3x squared minus 2x equals -5
Solving an Equation with a Square Root 2008-10-05
From Jonathan:
the square root of 3x+18 = x 3x+18 are within the square root
cos^2x - 3cosx = 1 2008-09-29
From Danielle:
cos2x - 3cosx = 1
Finding Traveling Time of a Projectile Given a Formula 2008-09-17
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
The Width of a Mown Strip of Lawn 2008-09-15
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?
y^2+3yz-8z-4z=0 2008-08-17
From Rae:
y^2+3yz-8z-4z=0
Two problems involving reciprocals 2008-08-10
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

algebra 2008-07-31
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 2008-07-30
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?
From Jeff:
c^2+4c+4

x^2-7x-18

A Falling Rock 2008-07-11
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
Sum and product of the roots of a quadratic 2008-07-03
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
(a-c)(b-c)(a+d)(b+d)=q^2-p^2
Regards
Gautam

3y^2 - 48 = 0 2008-06-23
From marquis:
3y^2 - 48 = 0
From Drew:
A solution of x^2-8x=-17 is

-4 or -4+I or 4 or 4+i

The area of a rectangle 2008-05-27
From Becky:
the area of a rectangular lot is represented by 6t^2+13t-5. What are the length and the width of the rectangular lot?
Factor and solve s1^2 - 10s1 - 200 = 0 2008-04-29
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 (3-i) and its complex conjugate 2008-04-22
From Tiffany:
Find the quadratic equation with roots at (3-i) and its complex conjugate.
A quadratic equation with odd coefficients 2008-04-15
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 .
A rectangle word problem 2008-04-10
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.
The product of the roots 2008-03-19
From Rebecca:
Determine the product of the roots of the equation (x-1)(x-2) + (x-2)(x-5)=0
The sum and product of the roots of a quadratic 2008-03-16
From Katelyn:

Sum of the roots = 16
Product of the roots = -80

(x^2+x-22)^4/3=16 2008-03-11
From Ryan:
(x^2+x-22)^4/3=16

I keep on getting thrown off because of the fractional exponent I couldn't find an example like this one

Completing the square 2008-03-11
From Ryan:
solve for x by completing the squares, x^2+4x-8=0
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 2007-12-11
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 yard-high wall.
Answered by Victoria West and Stephen La Rocque.
A quadratic function word problem 2007-11-12
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 + 21.4x-94.8
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.

Four triangles in a square 2007-10-15
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.
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 2007-10-07
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.
From Arlene:
Question from arlene, a student: x^+2x-24=0
Can you solve this by factoring? 10r^2 - 35r = 10 2007-08-12
From Aranxa:
how do u solve this equation by factoring:
10r^2 - 35r = 10

The domain and range of a quadratic function 2007-07-17
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)^2-3? 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 2007-06-29
From claire:
Find the range of values of k for which k(x^2+2x+3) - 4x - 2 is never negative.
The roots of (x - k)(1-3x) + 1 = 0 2007-06-28
From Claire:
Show that the roots of (x - k)(1-3x) + 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
15 = 19.2 t (time) - 4.9 t squared 2007-06-11
From Nicole:
15 = 19.2 t (time) - 4.9 t squared
From Stuart:
Solve the following quadratic equation: 3xsquared-5x-4=0
Using FOIL for (2x - 6)^2 2007-05-18
From TONI:
I am having a problem finding examples of how to solve (2x-6)^2.
Interval of the domain 2007-05-13
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 2007-04-14
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.
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
Intersection of a line and a circle 2007-04-12
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.
From Chin:
The quadratic equation y = (x-p)^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?
From Hector:
y=x^2-4x+3
y=x-1

Kicking a field goal 2007-03-13
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?
Maximize revenue 2007-03-08
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.
Finding the x-intercept 2007-03-02
From Ash:
Y = -1/100X^2 =27/10X +0 = 0 THE Y INTERCEPT IS 50 HOW DO I FIND THE X INTERCEPT
Fencing a field 2007-02-01
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?
y = x^2 - 2 2007-01-08
From Mike:
The area of a triangle 2006-12-29
From Paula:
The area of a triangle is 24cm². Its height is 2cm more than its base. Determine the base and the height.
From Harold:
L=3w-4
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
(3w-4) x w=96

could you give me an example

The roots of a quadratic equation 2006-11-16
From Lana:
If p and q are the roots of 2X^2 +3X+7=0, compute pq^3+qp^3. thanks for your help.
-3x squared + 5x -2=0 2006-11-14
From Stacey:
my son has a problem I am trying to figure out
neg 3x squared + 5x -2=0

Is this unsolvable? 2006-09-19
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 2006-09-10
From Lauren:

how do i factor

x3 - 6x2 + 8x

From Lynne:
What is wrong with this statement? "The quintic is one step up from the dread quadratic equation." (Newsweek, Dec. 19, 2005)
The perimeter of a regular octagon 2006-04-20
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?
From Miriam:

(x+2) (2x+3) = 6

6y^10 + 19y^5 + 14 2006-03-02
From Bahija:
Factor 6y10 + 19y5 + 14
Solve for x 2006-02-05
From Minti:
how can you solve for x?

f(x) = -1/4pi(x²) =10x -x²(4-pi)/8

Quadratic Equations & Given Roots 2005-11-11
From Lindsey:

I need to find the quadratic equation in the form:
f(x)=a(x2 - (-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?

How do you solve 3x^2 + x - 2 = 0 2005-09-15
From Lizzy:
How do you solve 3x2 + x - 2 = 0
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

x = (y^2 - b^2)/2b 2005-09-04
From Bob:
while looking at x=(y2-b2)/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=(y2-b2)/2b without pre knowing it is so?

Discriminant 2005-06-20
From A student:
If a quadratic has real root, its discriminant b2-4ac>=0 Is there any similar condition or method by which you can find whether roots of a cubic equation are real or not?
16x^2+20x-12x-15 2005-05-03
From Tanya:
how they got (4x+5)(4x-5) from
16x2+20x-12x-15=4x(4x+5)-3(4x+5)=(4x+5)(4x-5)

From Chris:

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....

From Jess:
6x+8=-x2
Solve for x 2005-02-02
From Christie:
Solve for x

.387 = (.40 - .265x)/(sqrt(1-x2))

cos 2x = sin x 2005-01-22
From Kris:
solve the equation
cos 2x = sin x for 0<= x < 360

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 e-mailed. 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.
An elliptical table 2005-01-03
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.
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))

x2 + x - 6 = 0

5y2 +19y = 3 10cos2 t + 3cos t = 4

Factoring 2004-11-09
From Rise:
Q1: a2 + 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 problem-solving technique did not help us to solve for the more complex problems as follows:

Q2: 9a3 - 24a2 + 12a

Factoring 2004-07-28
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?
x^2 = x + 2 2004-07-26
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.

From A student:
Could you please solve the following for x

x2+6=5x
x2+16=8x
2x+21=3x2

A tangent to a quadratic 2004-06-04
From Jem:
I have a question on the tangent to a quadratic curve. Say I have a curve y = ax2 + 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 y-axis where the tangent cuts isn't it? Is there a formula for it?

x^2/3 - 7 x^1/3 + 12 = 0 2004-04-05
From Jackie:
I am having trouble solving this question for x:

1.) x^2/3 - 7 x^1/3 + 12 = 0

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.
|x^2 - 12x| = 8 2004-01-24
From Sherre:
|x2 - 12x| = 8
The product of the page numbers 2003-11-07
From Morgan and Mom:
You open a book and the product of the page numbers is 12,656. What are your page numbers?
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 y-variable, 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.

x-6square root of x +8=0 2003-05-10
From Elizabeth:
x-6square root of x +8=0
Two intersecting graphs 2003-04-23
From Patty:

a) graph the equation

x2 - y - 4 = 0

x2 + y2 = 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.

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!:):):):):)

1. 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.
2. 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.
3. 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.

From Dan:
Why are equations of the form aX2 + bX + c =0 call quadratic? The quad indicates 4 but the power is 2.
The intersection of conics 2002-12-19
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.
From Katie:
just bugging the hell outta me and I cannot figure it out for the life of me.

1)x-2x-1 =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!

From Michael:
I would like to know, how to solve this Complex number: quadratic equation. ix 2 + x -i = 0
From Kathleen:

i have problems like

3x2 - 4x - 11 = 0 how do i work out that problem? i have the formula written down but it doesnt seem to register for me.

Factor 12x^2 - 20x - 8 2002-04-30
From Crystal:
Factor Completely: 12x2 - 20x - 8
A right-angled triangle 2001-12-13
From Pamela, Jeff, Kayleigh and Jacob:
A right-angled 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.
Solving x^2-3x+5=0 2001-11-30
From Katy:
How do you find the solution to x2-3x+5=0?
Why quadratic for a second degree equation? 2001-10-20
From Jana:
Why do we use the word quadratic to describe second degree equations?
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.
2. Do you find being a math expert very helpful in life?
3. Is the quadratic equation useful to you?
4. Why did you decide to become a math expert?
5. What do you think is the most important function of the quadratic equation?

25 y^2 + 20 y z - 4 z^2 2001-05-15
From Kimmy:
i don't know how to factor the trinomial 25y2 + 20yz - 4z2. 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.
From A parent:
A quadratic function is given by f:x------ax2+b

If the two points A(2, 2) and B (0, -8) are on the graph of the function, then find a and b.

Solving an equation 2001-03-27
From Jennifer:
How would I solve this equation? 1.6 = 2x/(.1-x) - 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.
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

The solutions of a quadratic 2001-01-30
From A student:
1. Show that the product of the solutions of ax2 + bx + c = 0 is c/a.

2. For each equation under the given condition, (a) find k and
(b) find the other solution.
kx2 - 2x + k = 0; one solution is -3

Completing the square 2001-01-12
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?

8x2 + 8x + 4

A problem with a quadratic 2000-08-09
From David Xiao:
Find the value of a such that 4x2 + 4(a-2)x - 8a2 + 14a + 31 = 0 has real roots whose sum of squares is minimum.
Finding a Quadratic Equation given the roots 2000-04-16
From A secondary student:
How do I find the equation for the quadratic with roots at 2-i and its complex conjugate?
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????

From Karen Johnson:
What is the reasoning behind the title quadratic equation?
Complex Roots 2000-01-24
From Jess Rutherford:
How do I find the value of k when 5x2 + k = 3x and has complex roots ?
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?
Two conics 1999-12-07
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."

2x2+2y2-8x+12y+16=0
.
.
.

Critical numbers 1999-11-17
From Sarah:
My question is this:

If f(x)=2x3+4x2-9x+8

and the derivative is f'(x)=6x2+8x-9,

how do I find the critical points if f'(x) is not factorable??

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

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?

From Ken Niebergall:
#1 a2 - 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 1999-03-25
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 1999-03-08
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?
Enlarging a Rink 1999-03-06
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 700m2 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.)

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)
Complex numbers and the quadratic formula 1998-12-25
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)

3x2+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?

From Fred Goodrich:
I need a step by step lesson on solving quadratic equations.

Thank you,

From Simon Batten:
How does varying the values a,b and c affect the graph of
y=ax2 + bx + c?

Find the Numbers. 1997-12-28
From Sandy C:
The sum of the squares of two numbers is 53. Twice the greater, minus the lesser is 11. Find the numbers.
Polynomials 1997-10-07
From Sheryl and Jeff:
I'm a math teacher in Jerusalem, Israel.

I'm teaching about graphing polynomial functions in a pre-calc class. A student asked me what they're good for. I couldn't give her a good example. Do you have one. Thanks.

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.