Please help solve the following problem:
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.
We can use $\displaystyle y=a(x-h)^{2}+k$
We are given that it passes through the point (29,11) and (50,0).
The vertex is at (h,k)=(0,k)
$\displaystyle 11=a(29-0)^{2}+k$
$\displaystyle 0=a(50-0)^{2}+k$
Solve for a and k. k is the value we want for the height at the center. The y-coordinate of the vertex.