Problema Solution

A rocket is fired upward from some initial distance above the ground. Its height in​ feet, h,above the​ ground, t seconds after it is​ fired, is given by hequals

minus16tsquaredplus96tplus3952

.

What is the​ rocket's maximum​ height?

Answer provided by our tutors

h(t) = -16t^2+96t+3952

We need to find h max.

The parabolic function h(t) = -16t^2+96t+3952 has maximum (since the quotient in front of t^2 is negative -16 < 0):

h max = c - b^2/(4a), where a = -16, b = 96, c = 3952

h max = 3952 - (96^2)/(4*(-16))

h max = 4096 ft

The rocket's maximum height is 4,096 ft.