h = -16t2 + 48t (v = initial velocity of 48 ft/sec)
Since the coefficient of the t2 term is negative (-16), the parabola opens downward and its vertex will be the highest point. The t-coordinate of the vertex is:
t(vertex) = -b/2a
Where a is the coefficient of the t2 term (-16) and b is the coefficient of the t term (48). Plug in the values to find the time it takes the rocket to reach its highest point, then plug that time into the h equation to determine the highest height.