The height of a baseball after its been hit is given by the following equation:

h(t) = -4.9t^2 + 29.4t + 1.5
Find the maximum height and time at which it occurs.

h(t) = -4.9t^2 + 29.4t + 1.5 => this is an inverted parabola, the vertex is the global maximum:
t = -29.4/-9.8 = 3
h(3) = -4.9 * 9 + 29.4 * 3 + 1.5 = 45.6 => max height

t = 3; h(t) = 45.6