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elixir [45]
2 years ago
14

I'm awarding 20 points for an answer!

Mathematics
1 answer:
Irina18 [472]2 years ago
4 0

Answer:

40 feet (after 1.5 seconds).

Step-by-step explanation:

The height h of the ball after t seconds is modeled by the function:

h(t)=-16t^2+48t+4

And we want to determine the ball's maximum height.

Since the given function is a quadratic, the maximum height occurs at the vertex point.

For quadratics, the vertex point is given by the formulas:

\displaystyle \Big(-\frac{b}{2a},f\Big(-\frac{b}{2a}\Big)\Big)

In this case, a = -16, b = 48, and c = 4.

Therefore, the t-coordinate at which the vertex occurs is:

\displaystyle t=-\frac{48}{2(-16)}=\frac{48}{32}=\frac{3}{2}

So, the maximum height occurs after 1.5 seconds.

Then the maximum height will be:

\begin{aligned}\displaystyle h\Big(\frac{3}{2}\Big)&=-16\Big(\frac{3}{2}\Big)^2+48\Big(\frac{3}{2}\Big)+4\\\\ &=-16\Big(\frac{9}{4}\Big)+24(3)+4\\\\&=-4(9)+72+4\\\\&=40\text{ feet}\end{aligned}

So, the maximum of the ball is 40 feet (after 1.5 seconds).

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