-16t2+63t+4

Question

The height h of an arrow in feet is modeled by h(t)=-16t2+63t+4, where t is the time in seconds since the arrow the shot. What is the maximum height of the arrow and after how long in the air will that maximum height occur?

 

Answer 1

This is a parabolic function. Therefore, the minimum or maximum will occur at the point where t = -b/2a.

 

b = 63

a = -16

 

t = -63/-32 = 63/32

 

The height at t=63/32 would be:

 

h(63/32) = -16(63/32)² + 63(63/32) + 4 = -3969/64 + 3969/32 + 4 = 4 + 3969/64 = 66.015625 feet