Complete the square with that equation. The maximum height occurs when the perfect squared term is zero.
This can be dome more easily with calculus, but you are apparently not studying that yet.
h(t) = -16t^2 + 384t + 4
= -16(t^2 -24t) -4 = 0
= -16(t^2 -24t + 144) +144 -4 = 0
= -16(t - 12)^2 + 140
h(max) = 140 when t = 12 s
The height of a rocket fired vertically into the air from the ground is given by the formula h(t) = -16t (2nd power) + 384t + 4, where t is measured in seconds. How long will it take to reach its maximum height and what is the maximum height reached by the rocket
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