parabolic arch.

Question

a bridge is built in the shape of a parabolic arch. The bridge arch has a span of 196 feet and a maximum height of 30 feet. find the height of the  arch at 15 feet from center.

Answer 1

Make the vertex (0, 30).

f(x) = ax² + 30

One x-intercept is (98, 0)

0 = a(98²) + 30

0 = 9604a + 30

-30 = 9604a

-30/9604 = a

 

f(x) = (-30/9604)x² + 30

 

Can you calculate for x = 15?