h(t)=-5(t+2)(t-20) where h(t) is the height in meters and t is the time in seconds after the launch.

Question

a) How high is the roof?

b) When will the rocket hit the ground?

c) What is the maximum height of the rocket?

d) when will the rocket reach the maximum height?

e) Graph the relation and label properly.

Answer 1

h = -5(t^2 -18t -40 = -5t^2 + 90t + 200. Roof is 200 meters high

0 = -5t^2 +90t +200 = -5(t+2)(t-20) =0 t=20 seconds when it hits the ground

take the derivative and set =0 to solve for time at max height

-10t +90 =0, t = 9 seconds. plug that into the original equation to get max height

-5(11)(-11) = 5(121) = 605 feet

It's a downward opening parabola, x or t intercepts at t=-2 and t=20. line of

symmetry is half way between them, at t = 9 vertex is the point (9,605) = max point on the graph