When a baseball is hit by a batter, the height of the ball, h(t), at time t, t = 0 is determined by the equation h(t) = -16t2 + 64t + 4 If t is in seconds, for which interval of time is the height of the ball greater than or equal to 52 feet?

We have the following equation:
 h (t) = -16t2 + 64t + 4
 We look for the time interval by means of the following inequality:
 -16t2 + 64t + 4> = 52
 Rewriting we have:
 -16t2 + 64t + 4 - 52> = 0
 -16t2 + 64t - 48> = 0
 -16 * (t-1) * (t-3)> = 0
 Solutions:
 t> = 1
 t <= 3
 Rewriting:
 1 <= t <= 3
 Answer:
 The height of the ball is greater than or equal to 52 feet in the interval:
 1 <= t <= 3