Answer:
h(7) = 784 ft
Explanation:
h(t) = -16t^2 + 224t
We want to find the maximum value for h
Factor out -16t
h(t) = -16t(t -14)
Set this equal to zero
0 = -16t(t -14)
-16t=0 t-14=0
t=0 t=14
The two zeros of the function are at 0 and 14
The vertex is 1/2 way between the two zeros
(0+14)/2 = 7
The vertex is at t =7
To find the maximum height we substitute t=7 into the equation
h(7) = -16*7(7 -14)
= -112 (-7)
=784