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parabola

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A Parabolic Arch 2020-09-21
Malen pose la question :
A hotel entrance makes a parabolic arch that can be represented by the quadratic function, y= -x^2-8x+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.
Harley Weston lui répond.
The flight of a football 2020-05-06
Michael pose la question :
Football is thrown from a 10-yard line. It reaches its highest height of 20 yards. It lands on the 50-yard 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.
Penny Nom lui répond.
A parabolic arch 2020-02-06
icyy pose la question :
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

Penny Nom lui répond.
A parabolic curve on a bridge 2019-03-09
monica pose la question :
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

Penny Nom lui répond.
A parabolic arch 2015-11-30
Muhammad pose la question :
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

Penny Nom lui répond.
A common tangent to two general parabolas 2015-11-15
Kind pose la question :
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.

Chris Fisher lui répond.
The flight of a ping pong ball 2015-10-13
Abigail pose la question :
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

Harley Weston lui répond.
The distance over a Quonset 2015-08-20
jane pose la question :
total base of hemisphere is 30 ft apex height is 20 feet what is total length over dome
Penny Nom lui répond.
A parabolic suspension bridge 2014-03-11
jeffrey pose la question :
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.
Penny Nom lui répond.
A parabola 2012-06-04
Madeline pose la question :
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.
Robert Dawson lui répond.
The parameterization of a parabola 2012-04-27
Shawna pose la question :
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?
Penny Nom lui répond.
A parabolic bridge 2012-04-24
Adiba pose la question :
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
Penny Nom lui répond.
A parabolic arch 2012-01-04
Swathi pose la question :
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

Penny Nom lui répond.
The graph of a quadratic function 2011-12-27
Thomas pose la question :
sketch a quadratic function with zeros at -3 and 1
Penny Nom lui répond.
The arc of a bridge 2011-12-05
Marioneta pose la question :
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.

Penny Nom lui répond.
A suspension bridge 2011-11-30
jennifer pose la question :
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.
Penny Nom lui répond.
A railway bridge over a road is in the shape of a parabola 2011-11-23
Brennen pose la question :
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!!

Penny Nom lui répond.
Will the ball clear the tree? 2010-11-14
MK pose la question :
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?
Brennan Yaremko lui répond.
The suspension cables of a bridge 2010-07-29
Mike pose la question :
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
Robert Dawson lui répond.
The equation of a parabola 2010-06-29
Tiffany pose la question :
Find the equation of a parabola that passes through the points (-2,3), (-1,1) and (1,9)
Stephen La Rocque lui répond.
Modelling an underpass 2010-05-11
Sue pose la question :
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.

Penny Nom lui répond.
Sketch the graphs of the following 2010-03-02
musaf pose la question :
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

Penny Nom lui répond.
The minimum point of a quadratic 2009-12-31
rachel pose la question :
y=0.0008x^2-0.384x
What is the minimum point of this equation?

Penny Nom lui répond.
A parabolic bridge 2009-10-03
SANDRA pose la question :
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

Stephen La Rocque lui répond.
A line tangent to a parabola 2009-10-01
kanchan pose la question :
for what value of c a line y=mx+c touches a parabola y^2=4a(x-a)
Penny Nom lui répond.
A parabolic arch 2009-03-28
Jeni pose la question :
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.

Penny Nom lui répond.
Graphing a parabola 2009-01-27
Kimberly pose la question :
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?
Penny Nom lui répond.
The parabola with vertex (7,-2) and directrix y = -3 2009-01-21
Deann pose la question :
Find an equation of the parabola with vetrex (7,-2) and directrix y =(-3)
Penny Nom lui répond.
Two tangent lines to a parabola 2008-10-26
Marcus pose la question :
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.
Penny Nom lui répond.
The vertex of a parabola 2008-09-30
Anne pose la question :
How do you find the vertex of the function f(x)=-x squared+7x-6
Penny Nom lui répond.
Finding Traveling Time of a Projectile Given a Formula 2008-09-17
David pose la question :
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
Janice Cotcher lui répond.
Graphing a parabola 2008-01-16
Sean pose la question :
How do I find the roots and describe the roots when graphing a parabola?

y = - x^2 - 4x -3

Stephen La Rocque lui répond.
Shooting an arrow over a wall 2007-12-11
Amy pose la question :
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.
Victoria West and Stephen La Rocque lui répond.
Completing the square 2007-11-01
Mark pose la question :
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.
Stephen La Rocque lui répond.
parabolic arch 2007-10-24
ABHILASH pose la question :
How find parabolic arch perimeter.
Harley Weston lui répond.
Parabolic suspension bridge 2007-10-09
Jessica pose la question :
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.)
Stephen La Rocque lui répond.
Parabolic arch 2007-10-09
Nisa pose la question :
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.
Stephen La Rocque lui répond.
The equation of a parabola 2007-10-02
srujana pose la question :
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?
Harley Weston lui répond.
x = y^2 and x = -4 y^2 2007-09-11
Jil pose la question :
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?
Penny Nom lui répond.
A parabola with vertex (-1,1) 2007-09-07
Ronaldinho pose la question :
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!
Stephen La Rocque and Penny Nom lui répond.
A chord of a parabola 2007-08-17
Robin pose la question :
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).
Penny Nom lui répond.
The domain and range of a quadratic function 2007-07-17
Linda pose la question :
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!
Stephen La Rocque and Penny Nom lui répond.
The Golden gate bridge 2007-06-17
Khan pose la question :
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.

Penny Nom lui répond.
Projectile motion equations 2007-06-12
Dillon pose la question :
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?
Stephen La Rocque lui répond.
Parabolas in the real world 2007-05-18
Katherine pose la question :
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!!
Stephen La Rocque lui répond.
Parabolas 2007-05-16
Andy pose la question :
How do you write an equation of a parabola that opens to the left with a vertex of (2,-6)?
Stephen La Rocque lui répond.
Finding a parabola's equation by looking at its graph 2007-04-30
Kenzie pose la question :
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.
Stephen La Rocque lui répond.
The equation of a parabola 2007-04-03
Suez pose la question :
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.
Stephen La Rocque lui répond.
The size of a parabolic transmitter/receiver 2007-03-26
Evan pose la question :
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!
Stephen La Rocque lui répond.
y = 1/4(x+3)^2-4 2007-03-17
Irene pose la question :
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.
Penny Nom lui répond.
A fountain as a parabola 2007-03-08
Emily pose la question :
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
Stephen La Rocque lui répond.
Things that are shaped like a parabola 2007-02-14
carra pose la question :
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:)
Steve La Rocque, Penny Nom and Walter Whiteley lui répond.
Can the trailer safely pass under the bridge? 2007-01-02
Jim pose la question :
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?
Stephen La Rocque lui répond.
Conic sections 2006-11-19
Joyce pose la question :
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.
Penny Nom lui répond.
The focus of a parabola 2006-10-01
Lily pose la question :
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?
Penny Nom lui répond.
How many items must the company produce to begin to make a profit? 2006-09-24
Devon pose la question :
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?
Stephen La Rocque lui répond.
What will the graph of y=x2 - 2x - 3 be? 2006-06-17
Byrony pose la question :
What will the graph of y=x2 - 2x - 3 be?
Steve La Rocque lui répond.
A fountain of water jets forms parabolic arches 2006-05-03
Jennifer pose la question :
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?
Stephen La Rocque lui répond.
A parabolic arch 2006-05-02
Mike pose la question :
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?
Stephen La Rocque lui répond.
The path of a submarine 2006-02-26
Meadow pose la question :
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.
Penny Nom lui répond.
One boundary of a pond is parabolic in shape. 2006-01-20
Glenn pose la question :
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.
Penny Nom lui répond.
Quadratic Equations & Given Roots 2005-11-11
Lindsey pose la question :

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?


Penny Nom lui répond.
A tangent to a parabola 2005-11-02
A student pose la question :
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)
Penny Nom lui répond.
A parabolic mirror 2005-05-24
Nathan pose la question :
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.
Penny Nom lui répond.
Quadratics 2005-01-05
Usman pose la question :
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.
Harley Weston lui répond.
Maximize income 2004-10-24
Connie pose la question :
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?

Penny Nom lui répond.
Practical applications: parabolas and Pythagoras 2004-10-24
Connie pose la question :
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.

Penny Nom lui répond.
Three parabolas 2004-04-24
A tutor pose la question :

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.


Penny Nom lui répond.
A parabolic arch 2004-01-19
Teresa and Robyn pose la question :
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
Penny Nom lui répond.
A parabola 2003-10-24
Delores pose la question :
Given the vertex (4, -2) y intercept = -6 find if/where the parabola crosses the x axis?
Penny Nom lui répond.
The cross-section of a football field 2003-05-25
Francis pose la question :
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.


Harley Weston lui répond.
A circle, tangent to two circles and a line 2003-04-30
Keith pose la question :
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.
Chris Fisher and Harley Weston lui répond.
Uses of conic sections 2003-04-01
William pose la question :
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.
Leeanne Boehm lui répond.
The intersection of conics 2002-12-19
Glenda pose la question :
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?
Chris Fisher and Harley Weston lui répond.
How do you estimate the equation of a parabola? 2002-12-01
Audrey pose la question :
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.
Penny Nom lui répond.
Determining a parabola 2002-11-06
Shelley pose la question :
let (0,3) and (1,9)and (-1,1) be given points in a parablola. Determine a b and c
Penny Nom lui répond.
A cone in 3 space 2002-03-20
Matthew pose la question :
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

.
.
.

Walter Whiteley lui répond.
Parabolas 2002-02-03
Kuang pose la question :
-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?


Harley Weston lui répond.
Quadratics 2001-05-16
John pose la question :
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?

Harley Weston lui répond.
Circles, ellipses, parabolas and hyperbolas 2001-05-09
Colleen pose la question :
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?

Pnny Nom lui répond.
Parabola problems 2001-04-10
Kathleen pose la question :
  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)

Harley Weston lui répond.
A suspension bridge 2001-03-24
Janna pose la question :
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?
Denis Hanson and Claude Tardif lui répond.

The path of a cannonball 2001-01-15
A student pose la question :
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.


Penny Nom lui répond.
Parabolas in life 2000-12-03
Ashley pose la question :
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!
Harley Weston lui répond.
Bridges and parabolas 2000-11-18
Lauren pose la question :
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.
Harley Weston lui répond.
The equation of a parabola 2000-05-22
Ian Forsyth pose la question :
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.
Penny Nom lui répond.
A parabola problem 2000-03-23
Morin pose la question :
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.
Penny Nom lui répond.
The Terror Run 2000-03-18
Danny Mclean pose la question :
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?


Harley Weston lui répond.
Parabolic mirrors 1999-11-07
Andy White pose la question :
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?
Penny Nom lui répond.

Parabolic shapes 1999-05-04
Justin Ailor pose la question :
Can you give me some parabolic shapes?
Penny Nom lui répond.
Satellite dishes 1999-02-10
Katherine Shaw pose la question :
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.
Jack LeSage and Harley Weston lui répond.
The Left Side of a Parabola. 1998-10-20
Shay pose la question :
Find the parametrized equation for the left half of the parabola with the equation: Y=x^2-4x+3
Chris Fisher lui répond.
Parabolas 1998-07-24
Danica pose la question :
how do you find the focus, vertex, and directrix of 4x-y^2-2y-33=0
Penny Nom lui répond.
Polynomials 1997-10-07
Sheryl and Jeff pose la question :
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.
Penny Nom lui répond.

The General Equation of a Parabola 1997-05-28
Michelle pose la question :
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
Harley Weston lui répond.

Parabolic Mirrors 1997-01-28
Megan Wennberg pose la question :
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.
Penny Nom lui répond.
 
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