# Find Parabola Equation

Discussion in 'Off-Topic Chat' started by nycmathguy, Aug 4, 2022.

1. ### nycmathguy

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I have trouble solving parabolic arc bridge questions.

Here's one:

A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Find the equation of the parabola. Then calculate the height of the arch at points 10 feet and 20feet from the center.

nycmathguy, Aug 4, 2022
2. ### MathLover1

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The equation of a parabola which opens down is

y - k= -A (x - h)^2, where (h, k) is the vertex (in your case, this is (0,25)) and A is a constant affecting the curvature

Thus your equation is just y = -Ax^2 + 25

Use one of the end-points of the arch such as (60, 0), to find the value of A. Then you have a suitable equation.

0 = -A*60^2 + 25
A = 1/144

equation is;

y = -(1/144)x^2 + 25

So plug x = 10, 20 into your equation and find your two corresponding heights.

y = -(1/144)10^2 + 25=875/36=24.3 feet

y = -(1/144)20^2 + 25=200/9=22.2feet
[B][/B]

MathLover1, Aug 4, 2022
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