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.

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) (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

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

So the equation of the parabola is

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....

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