Question

A model rocket is shot up from the roof of a school. The height at any time is modeled by the equation, H = -3t² + 12t + 36, where H is the height in metres and t is the time in seconds.
a) When does the rocket hit the ground?
b) How long does it take for the rocket to pass a window 21 metres above the ground?
c) What is the maximum height of the rocket?

Answer 1

a) when it hits the ground -3t² + 12t + 36 = 0
t^2 - 4t - 12 = 0
(t - 6)(t + 2) = 0
take over

b) -3t² + 12t + 36 = 21
t^2 - 4t - 5 = 0
this one also factors nicely, so keep grinding it out

c) H = -3t² + 12t + 36 is a parabola opening downwards, find the vertex and you got it