Answer:

To find the maximum height of the rocket, you need to determine the vertex of the parabolic function h(t) = 120t - 15t². The vertex of a parabola in the form of h(t) = at² + bt + c is given by the formula:

t = -b / (2a)

In this case, a = -15 and b = 120. Plug these values into the formula:

t = -120 / (2 * (-15))

t = -120 / (-30)

t = 4

Now that you know when the rocket reaches its maximum height (at t = 4 seconds), you can find the maximum height by plugging this value back into the original function h(t):

h(4) = 120(4) - 15(4)²

h(4) = 480 - 15(16)

h(4) = 480 - 240

h(4) = 240 feet

So, the maximum height of the rocket is 240 feet.

Step-by-step explanation:

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