







A Parabolic Arch 
20200921 

From Malen: A hotel entrance makes a parabolic arch that can be represented by the quadratic function, y= x^28x+24, where y is the height of the arch and x is the distance from wall to wall in the feet. What is the distance between the two walls of the arch. Answered by Harley Weston. 





The flight of a football 
20200506 

From Michael: Football is thrown from a 10yard line. It reaches its highest height of 20 yards. It lands on the 50yard line after 2 seconds. What is the equation of the parabola that models this throw? I really need help as I've been on this for the longest amount of time. Answered by Penny Nom. 





A parabolic arch 
20200206 

From icyy: how high is the parabolic arch of span 20 feet and height of 16 feet, at a distance 5 feet from the center?
what equation will I be going to use? thank you Answered by Penny Nom. 





A parabolic curve on a bridge 
20190309 

From monica: how do i fint the formula for my parabola with the provided information:
the golden gate bridge has a parabola
(343,160) = coordinate
(0,0)= vertex Answered by Penny Nom. 





A parabolic arch 
20151130 

From Muhammad: An arch over a road has a parabolic shape it is 6 meter wide at the base and is just
tall enough to allow a truck 5 meter high and 4 meter wide to pass
a):
assuming that the arch has an equation of the form y=a(x)^2+b use the given
information to find a & b. explain why this assumption is reasonable.
b):
sketch the graph of arch equation Answered by Penny Nom. 





A common tangent to two general parabolas 
20151115 

From Kind: Hi,
I want to find the common tangent of two general parabolas, but i don't know if it's possible or not.
If it's possible, please make a tutorial.
The first parabola equation : Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0.
The second parabola equation : Gx^2 + Hxy + Iy^2 + Jx + Ky + L = 0.
I need this because i want to find the equation of Beloch fold. (Huzita  Hatori 6th axiom)
However if you know any other method to find Beloch folds equation, I am open for any suggestions. Answered by Chris Fisher. 





The flight of a ping pong ball 
20151013 

From Abigail: Hello,
Wondering if there is a way to figure out the quadratic equation of half of a parabola?
Doing an assignment about finding quadratic equations for separate bounces of a ping pong ball, but the first bounce is incomplete (as the ball has presumably been dropped, hit the ground and then went on to make a complete bounce).
Please see attachment for references to the diagram that I am using.
Not sure whether I would have to look at it from a different perspective.
Thanks,
Abi Answered by Harley Weston. 





The distance over a Quonset 
20150820 

From jane: total base of hemisphere is 30 ft
apex height is 20 feet
what is total length over dome Answered by Penny Nom. 





A parabolic suspension bridge 
20140311 

From jeffrey: the towers of a parabolic suspension bridges 200 meter long are 40 meter high and the lowest point of the cable is 10 meter above the roadway.Find the vertical distance from the roadway to the cable at 50 meter from the center. Answered by Penny Nom. 





A parabola 
20120604 

From Madeline: In a parabola, I need to know what "a" b and c determine. I think that a determines the width of the parabola, but I am not exactly sure what b, and c do. Answered by Robert Dawson. 





The parameterization of a parabola 
20120427 

From Shawna: I am having problems finding the parameterization of a parabola. The question I was given is: Find the work done if a particle moves from the points (2,4) to (1,1) along the parabola y=x^2, while subject to the vector force of F=(x^3y,xy). So how would I start with finding the parameterization of a parabola? Answered by Penny Nom. 





A parabolic bridge 
20120424 

From Adiba: A bridge constructed over a bayou has a supporting arch in the shape of a parabola .Find the equation of the parabolic arch if the length of the road over the arch is 100 meters and the maximum height of the arch is 40 meters.
I did the problem but not sure is it correct .
I did like this f(0)=0we get c=40 if we took quadratic equation in x for a down ward parabola then how to find b and a please show me the answer of either a or b .Or I should use the standard form of parabola y=a(xh)^2+k then how to find a,h,k please help me 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. 





The arc of a bridge 
20111205 

From Marioneta: Two same columns placed symmetrically, 40 m apart.
The height of columns is 8 m.
If the origin of the coordinate system is placed at the foot
of the left column the equation of the arc of the bridge:
f (x) =1/80x^2+1/2x+8
What is the maximum height of a boat sailing under the bridge and
identify its path. Answered by Penny Nom. 





A suspension bridge 
20111130 

From jennifer: suspension bridges like the golden gate bridge, are used to span large distances.
when the main curved cables are attached to the deck by vertical cables they will end
up in the shape of parabola. assume that we need to build a bridge that spans
2,400 feet. the two towers 165feet tall each where placed at 400feet from either
side. the lowest point of the center of the bridge at 10feet. vertical suspension cables
where placed at 25foot interval. how many feet of cable are needed to connect
the deck to the main cables between the two towers? show all working. Answered by Penny Nom. 





A railway bridge over a road is in the shape of a parabola 
20111123 

From Brennen: A railway bridge over a road is in the shape of a parabola,
and the bridge is 3 m high in the middle and 6 m wide at its base.
A truck that is 2m wide is approaching the bridge.
What is the maximum height that the truck can have and
still pass under the bridge? Explain.
Thank you!! Answered by Penny Nom. 





Will the ball clear the tree? 
20101114 

From MK: Sam hits a golf ball with a fiveiron a distance of 120m horizontally. A tree 45m high and 35m in front of Sam is directly in the path of the ball. Will the ball clear the tree if the ball makes a parabolic curve and has a maximum height or 80m? Answered by Brennan Yaremko. 





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 equation of a parabola 
20100629 

From Tiffany: Find the equation of a parabola that passes through the points (2,3), (1,1) and (1,9) Answered by Stephen La Rocque. 





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. 





Sketch the graphs of the following 
20100302 

From musaf: without detailed plotting of points,sketch the graphs of the following
showing relevant information on the graphs:
a) y=(x3)2 +5
b)y=4xx2 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. 





A parabolic bridge 
20091003 

From SANDRA: a bridge is constructed across the river that is 200 feet wide. the arch is parabolic
so that the focus is on the water. A sheep 50 ft wide and 30 ft high passes safely
through the arch
a) find equation of the arch
*yk=(1/4)(xh)^2
b) find the highest point of the arch Answered by Stephen La Rocque. 





A line tangent to a parabola 
20091001 

From kanchan: for what value of c a line y=mx+c touches a parabola y^2=4a(xa) Answered by Penny Nom. 





A parabolic arch 
20090328 

From Jeni: A doorway is in the shape of a parabolic arch.
Find the width of the doorway 1m above the floor.
Given: the height and the width of the doorway is 4m and 3m respectively. Answered by Penny Nom. 





Graphing a parabola 
20090127 

From Kimberly: I need help with this parabola: graph y=5x^25x6. I am not really understanding how to graph parabolas in general. Can you help me? Answered by Penny Nom. 





The parabola with vertex (7,2) and directrix y = 3 
20090121 

From Deann: Find an equation of the parabola with vetrex (7,2) and directrix y =(3) Answered by Penny Nom. 





Two tangent lines to a parabola 
20081026 

From Marcus: Show that the tangent lines to the parabola y = ax^2 + bx + c at any two points with xcoordinates p and q must intersect at a point whose xcoordinate is halfway between p and q. Answered by Penny Nom. 





The vertex of a parabola 
20080930 

From Anne: How do you find the vertex of the function f(x)=x squared+7x6 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. 





Graphing a parabola 
20080116 

From Sean: How do I find the roots and describe the roots when graphing a parabola?
y =  x^2  4x 3 Answered by Stephen La Rocque. 





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. 





Completing the square 
20071101 

From Mark: An architect is designing a museum entranceway in the shape of a parabolic arch represented by the equation y = x2 + 20x, where 0 x 20 and all dimensions are expressed in feet. Determine the maximum height, in feet, of the arch. Answered by Stephen La Rocque. 





parabolic arch 
20071024 

From ABHILASH: How find parabolic arch perimeter. Answered by Harley Weston. 





Parabolic suspension bridge 
20071009 

From Jessica: A suspesion bridge with weight uniformly distributed along its length has twin towers
that extend 75 meters abouve the road surfce and are 400 meters apart.The cables are
parabolic in shape and are suspended from the tops of the towers. The cables touch the road
surface at the center of the bridge. Find the height of the cables at a point
100 meters from the center. (Assume that the road is level.) Answered by Stephen La Rocque. 





Parabolic arch 
20071009 

From Nisa: A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose suitable rectangular coordinate axes and find the equation of the parabola.
Then calculate the height of the arch at points 10 feet,20feet,and 40 feet from the center. Answered by Stephen La Rocque. 





The equation of a parabola 
20071002 

From srujana: Can we find the equation of the parabola when only two points on it are known and neither of them is the focus nor the vertex? Answered by Harley Weston. 





x = y^2 and x = 4 y^2 
20070911 

From Jil: My question is when dealing with parabolas, x=y^2, so that they are sifted on their side you could say,
what will happen to the graph if you change it to x=4y^2. I understand
that the  flips the graph in the other direction but can you simply just plug
in numbers and increase the stretch of the y? Answered by Penny Nom. 





A parabola with vertex (1,1) 
20070907 

From Ronaldinho: Hello. How do you find the equation of a parabola shown on a graph? i know the vertex is (1,1) and that's it. Thanks! Answered by Stephen La Rocque and Penny Nom. 





A chord of a parabola 
20070817 

From Robin: I am going to show that the chord PtPt' of the parabola has the equation 2xy(t+t')+2att'
A point on the parabola can be represented as Pt= (at2, 2at). Answered by Penny Nom. 





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. 





The Golden gate bridge 
20070617 

From Khan: I am doing a project on parabola and Bridges. I have chosen the Golden gate bridge
as my bridge. Now The suspension cables are shaped like a parabola.
We have to derive an equation for this parabola. We have to assume the vertex is
(0,0). Now I am having troubles writing the equation in standard form.
The information is this
Height of tower above water:
746 ft = 227 m
Height of tower above roadway:
500 ft = 152 m
Length of one side span: 1,125 ft = 343 m
length of suspension span including main span and side spans: 1.2 miles = 6,450 ft
Now my question is this, i KNOW THE standard form for this parabola opening up would
be (xh)squared = 4a (yk)
Since h,k are 0,0 the equation will now take the form of xsquared = 4ay
My question is to find the equation I need to know A how do i get this a based on the above
provided info. Thanks for your help and concern. Answered by Penny Nom. 





Projectile motion equations 
20070612 

From Dillon: Ron throws a ball straight up with an initial speed of 60 feet per second from a height of 5 feet. Find parametric equations that describe the motion of the ball as a function of time. How long is the ball in the air? When is the ball at its maximum height? What is the maximum height of the ball? Answered by Stephen La Rocque. 





Parabolas in the real world 
20070518 

From Katherine: Hi, my name is Katherine, and my mean old math teacher just assigned us a test in which
we have to write two examples of how parabolas are used in the real world, each one page
single spaced, size 12!! I know you have already answered some questions like this, but
I still don't understand the whole baseball thing, and any other way parabolas are used.
And how I can write a whole page on it. But that's my problem, not yours, I just need help
with a little explanation on how parabolas are actually used today. I know this might be kind
of confusing for you, but imagine how it is for me!! Answered by Stephen La Rocque. 





Parabolas 
20070516 

From Andy: How do you write an equation of a parabola that opens to the left with a vertex of (2,6)? Answered by Stephen La Rocque. 





Finding a parabola's equation by looking at its graph 
20070430 

From Kenzie: The graph shows an arrow going upward crossing at the 2 on the x line
and crossing the 3 on the x line and the vertex on the 6 on the y line. Answered by Stephen La Rocque. 





The equation of a parabola 
20070403 

From Suez: Find a parabola that passes through the point (1,4) and whose tangent lines at x= 1 and x= 5 have slopes 6 and 2 respectively. Answered by Stephen La Rocque. 





The size of a parabolic transmitter/receiver 
20070326 

From Evan: I am making a parabola for my home wireless LAN. I feel pretty confident
that I can make a parabolic trough that will work. But I am curious about
size. Is there really any advantage to using a deep (more depth) parabolic shape
over a shallow one as long as you use the correct focal point. And is bigger better?
I know that my parabola has to be bigger than the waves it is getting which
wont be a problem but if I make the diameter bigger does it get more effective or
is there such a thing as "too much of a good thing"? I have looked everywhere
for an answer and have come up short. Thanks! Answered by Stephen La Rocque. 





y = 1/4(x+3)^24 
20070317 

From Irene: How the graph of a parabola f(x)=1/4(x+3)squared4 can be obtained from the graph of y=xsquared, using Translations and Scalings. Answered by Penny Nom. 





A fountain as a parabola 
20070308 

From Emily: I have to do a math project proving that something in real life is a parabola. I really need some help here because i don't know where to start. I want to do it on a fountain and prove it's a parabola but how do i do that? I would really appreciate it if you could help Emily Answered by Stephen La Rocque. 





Things that are shaped like a parabola 
20070214 

From carra: i can't find other examples of things that are shaped like a parabola except for bridges.............. Pls. help it is due tomorrow. thank you very much:) Answered by Steve La Rocque, Penny Nom and Walter Whiteley. 





Can the trailer safely pass under the bridge? 
20070102 

From Jim: A truck hauling a doublewide trailer needs to pass under a parabolicarched bridge en route or take a 50 mile detour. The trailer is 14 feet high and 15 feet wide. The arch supporting the bridge at this underpass is 18 feet high at the center and 40 feet wide at the base. Can the trailer safely pass under the bridge? Answered by Stephen La Rocque. 





Conic sections 
20061119 

From Joyce: My son has a project on conic sections. I need the following information on Parabola, Circle, ellipse,and hyperbola. He can't find the following information for each conic section: equations with explanations, four uses for each shape and Shape explanation. Answered by Penny Nom. 





The focus of a parabola 
20061001 

From Lily: I have a mathematical assignment which includes applications of parabolas, hyperbolas and ellipses in the real world. I have been searching the internet and now I am ware that most of the applications of parabolas have a connection with what people call "the focus". However, I do not think I clearly understand what "the focus" of a parabola is. Would you please explain it to me? Answered by Penny Nom. 





How many items must the company produce to begin to make a profit? 
20060924 

From Devon: The profit a manufacturing company makes can be found using the formula
P=120n  n^2  2200
How many items must the company produce to begin to make a profit? Answered by Stephen La Rocque. 





What will the graph of y=x2  2x  3 be? 
20060617 

From Byrony: What will the graph of y=x2  2x  3 be? Answered by Steve La Rocque. 





A fountain of water jets forms parabolic arches 
20060503 

From Jennifer: Let's say in you have a fountain and the water jets form parabolic arches. The center of the fountain, being the origin of the coordinate system, it is elevated 5 feet off the ground, . The equation formed the water arch is y= x^{2}+4x, what is the radius of the basin needed to catch the water at ground level? Answered by Stephen La Rocque. 





A parabolic arch 
20060502 

From Mike: A bridge over a river is supported by a parabolic arch...arch is 200 m wide at water level...the maximum height of the arch is 80 m..what is the height of the arch measured from a point on the water 40m from the center of the arch? Answered by Stephen La Rocque. 





The path of a submarine 
20060226 

From Meadow: Suppose that a submarine has been ordered to follow a path that keeps it equidistant from a circular island of radius r and a straight line shoreline that is 2 units from the edge of the island. Derive an equation of the submarine path, assuming that the shoreline has equation x = p and that the center of the island is on the xaxis. Answered by Penny Nom. 





One boundary of a pond is parabolic in shape. 
20060120 

From Glenn: One boundary of a pond is parabolic in shape. The boundary passes through the points A(20,45), B(40,40) and E(30,35). The equation of the parabola is of the form y=ax2+bx+c. Find the equation of the parabola and the coordinates of the vertex of the parabola. Any assistance you could provide would be greatly appreciated. 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. 





A tangent to a parabola 
20051102 

From A student: Find the point on the curve y=x^{2} where the tangent to the curve is parallel to the secant line connecting (1,1) and (2,4) Answered by Penny Nom. 





A parabolic mirror 
20050524 

From Nathan: i am trying to find the equation for a mirror for a laser experiment. the mirror is parabolic but my question is how do you find the equation when you know only the focus and the diameter the mirror diameter is 520 mm and the focus is at 1024 mm. would you just use the measurements in the equation instead of "nice numbers" or what. 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. 





Maximize income 
20041024 

From Connie: A company that sells x units of a product generates an income (I, in dollars) which is a function of x. The income generated is described by the equation
I = (1/2)x^2 + 100x.
Discuss how to determine the number of units that must be sold so that the company can maximize its income. What is the maximum income? Answered by Penny Nom. 





Practical applications: parabolas and Pythagoras 
20041024 

From Connie: Provide two examples of real life objects that incorporate parabolic shapes. Explain the reason why the parabolic shape was used in each object.
I need at least one practical application of the Pythagorean Theorem. Answered by Penny Nom. 





Three parabolas 
20040424 

From A tutor:
I am a maths tutor. One of my year 12 students has given me this assignment. Many parts are ambiguous.
I am trying to determine the equation of the line segment AB. Given that A has an incline of 10 degrees below the horizontal, I am assuming that this parabola (although you can only see part of it) has been rotated 10 degree clockwise. Am I right in assuming this? If so, how do I derive the equation of the parabola as it will then not fit the general form y = ax squared +bx +c of a parabola.
Also, how is one expected to find the x coordinate of D without the equation of this parabola. To find the equation you need the xcoordinate and therefore be able to find another point on the parabola in order to derive the equation using simultaneous equations.
Answered by Penny Nom. 





A parabolic arch 
20040119 

From Teresa and Robyn: A bridge over a river is supported by a parabolic arch...arch is 200 m wide at water level...the maximum height of the arch is 80 m..what is the height of the arch measured from a point on the water 40m from the centre of the arch Answered by Penny Nom. 





A parabola 
20031024 

From Delores: Given the vertex (4, 2) y intercept = 6 find if/where the parabola crosses the x axis? Answered by Penny Nom. 





The crosssection of a football field 
20030525 

From Francis: Have you ever walked on a football field covered with artificial turf? If so, you probably noticed that the field is not flat. The profile of the surface is arched and highest in the centre, permitting rainwater to drain away quickly. height from base to highest point 45.75 centimetres distance of the field 50 metres a) The diagram shows the profile of an actual field, viewed from the end of the field. Assuming that the crosssection is a parabola, find the algebraic model that describes this shape. b) Use your equation to determine the distance from the sidelines where the field surface is 20 cm above the base line. Answered by Harley Weston. 





A circle, tangent to two circles and a line 
20030430 

From Keith: I have a horizontal line (that is treated as a datum line or the X axis), with two circles having their center points at different heights from that line (X1,Y1 & X2,Y2). The two circles are also at different diameters (R1 & R2). Both circles and the line (XAxis) do not intersect nor are they tangent. My goal is to determine the maximum diameter of an inscribed circle that will fit between all three. Answered by Chris Fisher and Harley Weston. 





Uses of conic sections 
20030401 

From William: My name is William and I am doing a research paper on conic sections for my 12th grade math class. Part of the project is to find two conic sections in our world today and explain what there purpose is. I really need help in this area because I've been searching the internet for where conic sections are used in our world today and I really can't find anything. If you can tell me specific building or a pyramid that contains conic sections that would be great. Or even something in the universe would be helpful. Answered by Leeanne Boehm. 





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. 





How do you estimate the equation of a parabola? 
20021201 

From Audrey: How do you estimate the equation of a parabola? I have a project where a must find parabolas in magazines and then estimate their equation. Answered by Penny Nom. 





Determining a parabola 
20021106 

From Shelley: let (0,3) and (1,9)and (1,1) be given points in a parablola. Determine a b and c Answered by Penny Nom. 





A cone in 3 space 
20020320 

From Matthew: Let C in R^{3} be the cone defined by x^{2} + y^{2}  z^{2} = 0 (A) Let P be the plane described by x + 2z = 1 (i) Find a description of P in terms of two parameters s and t . . . Answered by Walter Whiteley. 





Parabolas 
20020203 

From Kuang: Who is credited for working with or studying the Parabola? What is a conic section? What does a parabola look like? How is a parabola formed? Where and how are parabolas used today in the real world? Answered by Harley Weston. 





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. 





Circles, ellipses, parabolas and hyperbolas 
20010509 

From Colleen: How is an ellipse like a circle? In what way does an ellipse have a center? How is a hyperbola similar and different to an ellipse? How is a parabola similar a different to a circle ellipse and parabola? Answered by Pnny Nom. 





Parabola problems 
20010410 

From Kathleen:
 Graph each function and state its domain and range. y = 3x^{2} + 4
 For each parabola find: i) the direction of opening
ii) the coordinates of the vertex iii) the yintercept iv) the xintercepts y = x^{2} + 3
 Find the equation of each parabola vertex at (0, 2) and passing through the point (3,7)
Answered by Harley Weston. 





A suspension bridge 
20010324 

From Janna: The cables of a suspension bridge hang in a curve which approximates a parabola. The road bed passed through the vertex. If the supporting towers are 720m apart and 60m high, find: a) an equation of the parabola (it's y = ^{1}/_{2160}x^{2}) b)the height of the cables at a point 30m from the vertex. I substituted 30 in for the x value and got 0.42 and the answer is 42. What did I do wrong? Answered by Denis Hanson and Claude Tardif. 





The path of a cannonball 
20010115 

From A student: Artillerymen on a hillside are trying to hit a target behind a mountain on the other side of a river. Their cannon is at (x, y) = (3, 250) where x is in kilometers and y is in meters. The target is at (x, y) = (2, 50). In order to avoid hitting the mountain on the other side of the river, the projectile from the cannon must go through the point (x, y) = (1, 410). Write the equation for the problem. Answered by Penny Nom. 





Parabolas in life 
20001203 

From Ashley: I am a student and my teacher recently gave us the assignment of writing a portfolio on parabolas in life and finding examples, three to be in fact, only we have to go into detail about only one. We have been instructed to include such terms as: axis of symmetry, completing the square, parabola, quadratic formula, standard form (vertex form) and vertex. We also must include in our detailed example an equation of the parabola and very specific details, PLEASE HELP! Answered by Harley Weston. 





Bridges and parabolas 
20001118 

From Lauren: My name is Lauren, and Im a secondary school student in Ontario. For my gr11 advanced math class I have to find out how and why parabolics are used in arch bridges and write 3 paragraphs on it. People who cohse satelites and whatnot are lucky  I've found a ton of info, but for arch bridges there seems to be nothing. Answered by Harley Weston. 





The equation of a parabola 
20000522 

From Ian Forsyth: Given the points A(0,0) B(60,10) C(24,d) find the equation of the parabola. leave the equation in terms of x, y and d if the general form of a quadratic is y = ax^{2} + bx + c. Answered by Penny Nom. 





A parabola problem 
20000323 

From Morin: I need to prove that if parabola x^{2}=4py has a chord (not necessarily a focal chord) intersecting it at points A and B, with tangents to the parabola at points A and B that intersect at C, then a line drawn through C and the midpoint of the chord M is parallel to the yaxis. Further, prove that the point D where this line intersects the parabola is the midpoint of line CM. Answered by Penny Nom. 





The Terror Run 
20000318 

From Danny Mclean: A fairground's most popular attraction is a roller coaster ride known as the Terror Run. One stretch of track is called the Missile Path and is in the form of a parabolic curve. B is 180m horizontally from A and the highest point of the curve is 100m above A and B. A.. The owner works out a quadratic expression to describe the Missile Path. What is the expression He found? B.. A safety Engineer examined the structure and observed that points A and B were likely to be damaged due to the steepness of the Missile path near these points. The owner can see no way to make the Missile path less steep near A and B and to keep the height of the ride the same. HOW CAN IT BE DONE? Answered by Harley Weston. 





Parabolic mirrors 
19991107 

From Andy White: I am working on a project concerning parabolic mirrors. I need to create a mirror to focus sunlight on a focal point, but I don't know how to do it. Is there some equation that tells where a focal point will be in relation to a parabola? What is a directrix? Answered by Penny Nom. 





Parabolic shapes 
19990504 

From Justin Ailor: Can you give me some parabolic shapes? Answered by Penny Nom. 





Satellite dishes 
19990210 

From Katherine Shaw: I have read your information on 'Why are satellite dishes parabolic", and I know the reciever should be placed at the focus of the parabola. Could you test this with lights beams and a parabolic mirror, or would light beams behave differently. Thanks. Answered by Jack LeSage and Harley Weston. 





The Left Side of a Parabola. 
19981020 

From Shay: Find the parametrized equation for the left half of the parabola with the equation: Y=x^24x+3 Answered by Chris Fisher. 





Parabolas 
19980724 

From Danica: how do you find the focus, vertex, and directrix of 4xy^22y33=0 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. 





The General Equation of a Parabola 
19970528 

From Michelle: My name is Michelle and I am a 10th grade student in algebra 2 w/ analysis. I am doing a report on parabolas and I need to know what the general equation is. I've looked in books and keep finding different ones! I also need to know how they can be used in nature. Thank you so much for your time. I really appreciate it!  Michelle Answered by Harley Weston. 





Parabolic Mirrors 
19970128 

From Megan Wennberg: Consider a ray of light that passes through a chord of a parabola (the chord is above the focus and parallel to the directrix), hits the parabola at a point (x,y) and is reflected through the focus. If d1 is the distance from the chord to the point of incidence (x,y) and d2 is the distance from (x,y) to the focus, can you prove that the sum of the distances d1+d2 is constant, independent of the particular point of incidence. Answered by Penny Nom. 

