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parabola

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A parabolic arch 2015-11-30
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 2015-11-15
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 2015-10-13
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 2015-08-20
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 2014-03-11
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 2012-06-04
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 2012-04-27
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,x-y). So how would I start with finding the parameterization of a parabola?
Answered by Penny Nom.
A parabolic bridge 2012-04-24
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(x-h)^2+k then how to find a,h,k please help me
Answered by Penny Nom.
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

Answered by Penny Nom.
The graph of a quadratic function 2011-12-27
From Thomas:
sketch a quadratic function with zeros at -3 and 1
Answered by Penny Nom.
The arc of a bridge 2011-12-05
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 2011-11-30
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 2011-11-23
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? 2010-11-14
From MK:
Sam hits a golf ball with a five-iron 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 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
Answered by Robert Dawson.
The equation of a parabola 2010-06-29
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 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.

Answered by Penny Nom.
Sketch the graphs of the following 2010-03-02
From musaf:
without detailed plotting of points,sketch the graphs of the following showing relevant information on the graphs:
a) y=(x-3)2 +5
b)y=4x-x2

Answered by Penny Nom.
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?

Answered by Penny Nom.
A parabolic bridge 2009-10-03
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
*y-k=(-1/4)(x-h)^2
b) find the highest point of the arch

Answered by Stephen La Rocque.
A line tangent to a parabola 2009-10-01
From kanchan:
for what value of c a line y=mx+c touches a parabola y^2=4a(x-a)
Answered by Penny Nom.
A parabolic arch 2009-03-28
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 2009-01-27
From Kimberly:
I need help with this parabola: graph y=5x^2-5x-6. 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 2009-01-21
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 2008-10-26
From Marcus:
Show that the tangent lines to the parabola y = ax^2 + bx + c at any two points with x-coordinates p and q must intersect at a point whose x-coordinate is halfway between p and q.
Answered by Penny Nom.
The vertex of a parabola 2008-09-30
From Anne:
How do you find the vertex of the function f(x)=-x squared+7x-6
Answered by Penny Nom.
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
Answered by Janice Cotcher.
Graphing a parabola 2008-01-16
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 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.
Completing the square 2007-11-01
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 2007-10-24
From ABHILASH:
How find parabolic arch perimeter.
Answered by Harley Weston.
Parabolic suspension bridge 2007-10-09
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 2007-10-09
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 2007-10-02
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 2007-09-11
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) 2007-09-07
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 2007-08-17
From Robin:
I am going to show that the chord PtPt' of the parabola has the equation 2x-y(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 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.
The Golden gate bridge 2007-06-17
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 (x-h)squared = 4a (y-k)

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 2007-06-12
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 2007-05-18
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 2007-05-16
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 2007-04-30
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 2007-04-03
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 2007-03-26
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)^2-4 2007-03-17
From Irene:
How the graph of a parabola f(x)=1/4(x+3)squared-4 can be obtained from the graph of y=xsquared, using Translations and Scalings.
Answered by Penny Nom.
A fountain as a parabola 2007-03-08
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 2007-02-14
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? 2007-01-02
From Jim:
A truck hauling a double-wide trailer needs to pass under a parabolic-arched 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 2006-11-19
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 2006-10-01
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? 2006-09-24
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? 2006-06-17
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 2006-05-03
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= -x2+4x, what is the radius of the basin needed to catch the water at ground level?
Answered by Stephen La Rocque.
A parabolic arch 2006-05-02
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 2006-02-26
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 x-axis.
Answered by Penny Nom.
One boundary of a pond is parabolic in shape. 2006-01-20
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 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?


Answered by Penny Nom.
A tangent to a parabola 2005-11-02
From A student:
Find the point on the curve y=x2 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 2005-05-24
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 2005-01-05
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.
Answered by Harley Weston.
Maximize income 2004-10-24
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 2004-10-24
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 2004-04-24
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 x-coordinate 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 2004-01-19
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 2003-10-24
From Delores:
Given the vertex (4, -2) y intercept = -6 find if/where the parabola crosses the x axis?
Answered by Penny Nom.
The cross-section of a football field 2003-05-25
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 cross-section 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 2003-04-30
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 (X-Axis) 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 2003-04-01
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 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.
How do you estimate the equation of a parabola? 2002-12-01
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 2002-11-06
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 2002-03-20
From Matthew:
Let C in R3 be the cone defined by x2 + y2 - z2 = 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 2002-02-03
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 2001-05-16
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.
  1. How do you use quadratic equations in your everyday life?
  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?

Answered by Harley Weston.
Circles, ellipses, parabolas and hyperbolas 2001-05-09
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 2001-04-10
From Kathleen:
  1. Graph each function and state its domain and range. y = 3x2 + 4

  2. For each parabola find: i) the direction of opening
    ii) the coordinates of the vertex
    iii) the y-intercept
    iv) the x-intercepts
    y = x2 + 3

  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 2001-03-24
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 = 1/2160x2)

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 2001-01-15
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 2000-12-03
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 2000-11-18
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 2000-05-22
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 = ax2 + bx + c.
Answered by Penny Nom.
A parabola problem 2000-03-23
From Morin:
I need to prove that if parabola x2=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 y-axis. 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 2000-03-18
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 1999-11-07
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 1999-05-04
From Justin Ailor:
Can you give me some parabolic shapes?
Answered by Penny Nom.
Satellite dishes 1999-02-10
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. 1998-10-20
From Shay:
Find the parametrized equation for the left half of the parabola with the equation: Y=x^2-4x+3
Answered by Chris Fisher.
Parabolas 1998-07-24
From Danica:
how do you find the focus, vertex, and directrix of 4x-y^2-2y-33=0
Answered by Penny Nom.
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.
Answered by Penny Nom.

The General Equation of a Parabola 1997-05-28
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 1997-01-28
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.
 
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