Question

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(t)=-16t^2+48t , where t is the time in seconds since the rocket was shot and f(t) is the rocket’s height. What is the maximum height the rocket reaches?

16ft
36ft
48ft
or 144 ft

Answer 1

Well, that is a parabola. Where is the vertex?

-16 t^2 + 48 t = h

16 t^2 - 48 t = -h

t^2 - 3 t = -(1/16)h

t^2 - 3 t + 9/4 = -(1/16)h + 9/4

(t - 3/2)^2 = -(1/16)(h - 36)

ah ha, hits the vertex at the top when t = 1.5 seconds and h = 36 feet

Answer 2

thanks!!

Answer 3

You are welcome.