SOLUTION: A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 152 feet and a maximum height of 35 feet. Find the height of the arch at 25 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 152 feet and a maximum height of 35 feet. Find the height of the arch at 25 feet from its center.      Log On


   

Question 1155249: A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 152 feet and a maximum height of 35 feet. Find the height of the arch at 25 feet from its center.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let the origin be center of the base of the arch. The vertex of the parabola is then at (0,35); and two points on the parabola are (-76,0) and (76,0).

The equation of the parabola is of the form

y+=+35-ax%5E2

where the value of the coefficient a is determined by the point (76,0) on the parabola.

0+=+35-a%2876%5E2%29
a%2876%5E2%29+=+35
x+=+35%2F76%5E2

So the equation of the parabola is

y+=+35-%2835%2F76%5E2%29x%5E2

graph%28800%2C200%2C-80%2C80%2C-10%2C40%2C35-%2835%2F76%5E2%29x%5E2%29

To find the height of the arch 25 feet from its center, simply find the value of y when x is 25.

I leave that much of the problem for you....