Question

The trajectory of a rocket is represented by the function h(t) = -3t2 + 24t + 36, where h is height in meters and t is time in seconds.

At what time does the rocket reach its maximum height?

Answer 1

You merely want the vertex of the typical parabola
for y = ax^2 + bx + c, the x of the vertex is -b/(2a)

so for yours, the t of the vertex is -24/(-6) = 4

the max height is reached after 4 seconds