Question

A stone is thrown straight up from the roof of an 80 ft building. the height, in feet, of the stone at any time t, in seconds, measured from the ground is given by ℎ(????) = −16???? 2 + 64???? + 80. what is the maximum height the stone reaches?

Answer 1

144 ft

Step-by-step explanation:

h(t) = -16t² + 64t + 80

The maximum height is at the vertex. We can find the vertex of a parabola using -b / (2a):

t = -64 / (2×-16)

t = 2

The vertex is at 2 seconds. The height of the stone at this time is:

h(2) = -16(2)² + 64(2) + 80

h(2) = 144

The maximum height is 144 feet.