Question

PLS HELP WILL MARK BRAINLIEST. IF GOTTEN RIGHT SHOW WORK

Answer 1

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