# 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.

Seeking a step-by-step reply.

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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