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. after how many seconds does the ball reach its maximum height? what is the maximum height of the ball? after how many seconds does it reach the ground?

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