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

Although your question is incomplete and the expression is a little incorrect, I have seen it before.
h(t) = -0.2t² + 2t
In order to find the maximum height, we first differentiate the expression and then set the derivative equal to 0. Thus:
0 = -0.4t + 2
t = 5 seconds

The ball reaches its maximum height at 5 seconds

The ball reaches the ground again when h(t) = 0
0 = -0.2t² + 2t
t(-0.2t + 2) = 0

t = 0 ; t = 10

Therefore, the ball reaches the ground when time is 10 seconds