SOLUTION: A parabolic arch has a span of 100 feet and a maximum height of 25 feet. Write an equation to represent the arch, then calculate the height of the arch 20 feet from the center

Hi

A parabolic arch has a span of 100 feet and a maximum height of 25 feet. 

Using the vertex form of a parabola,  where(h,k) is the vertex

  y = a(x-50)^2 + 25  Vertex (50,25)

  0 = a50^2 + 25   |Using x-intercept Pt(0,0) to solve for a

 -25/2500 = a

  y = (-1/100)(x-50)^2 + 25

 height of the arch 20 feet from the center: 

 x = 30

 y = (-1/100)20^2 + 25

 y = -4 + 25

 y = 21ft