The following quadratic function describes a launched Air Force missiles height over time is h(t)=-t^2+6t. a. Why is it important to know the zeros of the function? what do the zeros tell us?
b. How long was the missile in flight for?
c. what was the maximum height reached by the missile?
d. The early warning system alarmed when the missile was descending and reached the height of 8 km. how much time is there before impact?

See below.

Step-by-step explanation:

a) The zeros tell us when the missiles will be at ground level after being launched.

b) h(t) = 0 = -t^2+6t = t(6-t)

The missile was in flight for 6 units minutes.

c) h'(t) = -2t+6 = 0 --> t = 3

h(3) = 9

d) 8 = -t^2+6t

t^2-6t+8 = 0

(t-2)(t-4)=0

The missile is descending at a height of 8 km at 4 minutes.

It lands at 6 minutes.  So, it will impact 2 minutes after the early warning alarm.

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