SOLUTION: A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 174 feet and a maximum height of 27 feet. Find the height of the arch at 12 feet from its center

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 174 feet and a maximum height of 27 feet. Find the height of the arch at 12 feet from its center       Log On


   

Question 1105272: A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 174 feet and a maximum height of 27 feet. Find the height of the arch at 12 feet from its center

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
So in the middle where x=0, y=27.
At the edges where x=174%2F2=87 and at x=-87, y=0
Using the general vertex form,
y=a%28x-0%29%5E2%2B27
When x=87,
0=a%2887%29%5E2%2B27
a=-27%2F87%5E2
a=-27%2F7569
So,
y=-%2827%2F7569%29x%5E2%2B27
When x=12,
y=-%2827%2F7569%29%2812%29%5E2%2B27
y=-3888%2F7569%2B27
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