Question

The height of a toy rocket that is shot in the air with an upward velocity of 48 feet per second can be modeled by the function f (x) = negative 15 t squared 48 t, where t is the time in seconds since the rocket was shot and f(t) is the rocket’s height in feet. what is the maximum height the rocket reaches?

Answer 1

The maximum height of an object is the greatest height the object can reach. The maximum height the rocket reaches is 40.2 feet

Vertex form of an equation

The maximum height of an object is the greatest height the object can reach. Given the equation that represent the height of the rocket.

f(t) = -15t² + 48t

The maximum height of the rocket occur at the point where:

t = -b/2a
t = -48/2(-15)
t =48/30
t = 1.6secs

Substitute t = 1.6 into the function as shown:

f(1.6) = -15(1.6)² + 48(1.6)

f(1.6) = -38.4 + 76.8

f(1.6) = 40.2

Hence the maximum height the rocket reaches is 40.2 feet

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