quadratic equation math problem?

Question

A bridge is supported by three arches. The function that describes the arches is

h(x)=-0.25x^2+2.375x

where h(x) is the height, in metres, of the arch above the ground at any distance, x, in metres, from one end of the bridge. 

How far apart are the bases of each arch?

Answer 1

Set the ground as the x-axis, with the one end at the origin, 

then find where the curve crosses:

h(x) = -0.25x² + 2.375x = 0

x(-0.25x + 2.375) = 0

x = 0 

and

-0.25x + 2.375 = 0

-0.25x = -2.375

x = -2.375 / -0.25

x = 9.5

The bases are 9.5 meters apart.