h(t) = - 16t^2 + 48t
factor
16t(3-t)
The vertex is in the middle of t =0 and t =3, ⇒ t = 1.5
That is the symmetry axis, t =1.5
It represents the time at which the ball stops going up and starts going down, this is where it reaches the maximum height.
Answer : a. t = 1.5; it takes 1.5 seconds to reach the maximum height and 3 seconds to fall back to the ground