Answer:
D. 1024 feet
Step-by-step explanation:
The height function can be written in vertex form as ...
f(t) = -16(t -2)^2 +1024
This has a maximum value of 1024 (feet) at t=2 (seconds).
The maximum height of the ball is 1024 feet.
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Rearranging to vertex form can be accomplished in a few steps:
-16(t^2 -4t) +960 . . . . . factor the leading coefficient from the variable terms
-16(t^2 -4t +4) +960 -(-16)(4) . . . . . add and subtract the square of half the linear term coefficient: (4/2)^2 = 4
-16(t -2)^2 +1024 . . . . . collect terms and put into vertex form
