Question

Suppose h(t)= -0.2t^2+2t models the height, in feet, of a ball that is kicked into the air where t is given as time, in seconds.

Answer 1

This function is a parabola with the vertex giving the max height, h and time t. vertex = (-b/2a, h)
t = -b/2a
t = -2/-0.4
t = 5 seconds

If you enter that for t then solve for maximum height h.
h = -0.2(5)² + 2(5)
h = -0.2(25) + 10 
h = -5 + 10
h = 5 ft

If it takes 5 seconds to reach max height it will take another 5 seconds to reach the ground. 5+5 = 10 seconds