# Math Help - semielliptical arch

1. ## semielliptical arch

A bridge is built in the shape of a semielliptical arch. It has a span of 100 feet. The height of the arch 29 feet from the center is to be 11 feet. Find the height of the arch at its center.

2. We can use $y=a(x-h)^{2}+k$

We are given that it passes through the point (29,11) and (50,0).

The vertex is at (h,k)=(0,k)

$11=a(29-0)^{2}+k$

$0=a(50-0)^{2}+k$

Solve for a and k. k is the value we want for the height at the center. The y-coordinate of the vertex.