9514 1404 393
Answer:
12 feet
Step-by-step explanation:
You seem to have a few of these, so let's find a generic solution.
The vertex form of a quadratic equation is ...
f(x) = a(x -h)² +k
When we expand that, we get ...
f(x) = a(x² -2hx +h²) +k = ax² -2ahx +ah² +k
Comparing this to your standard form quadratic ...
h(t) = -16t² +vx +s
we can see that ...
- a = -16
- -2ah = v
- ah² +k = s
Solving for h and k, we get ...
(-2)(-16)h = v
h = v/32
and
k = s -ah² = s -(-16)(v/32)²
k = s +v²/64
So, the generic solution for these problems is ...
h = time to maximum height = v/32
k = maximum height = s +v²/64
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This problem asks for the maximum height, which will be ...
s +v²/64 = 3 +24²/64 = 3 +9 = 12 . . . . feet
