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.

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- Dec 4th 2008, 06:45 PManaanaasemielliptical arch
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. - Dec 4th 2008, 08:14 PMgalactus
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.