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?

Question

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.