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2 months ago

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A pebble is tossed into the air from the top of a cliff. The height, in feet, of the pebble over time is modeled by the equation

y = -16x^2 + 32x + 80. What is the maximum height, in feet, reached by the pebble?
The maxium height is _____ feet.

1 answer:

PIT_PIT [12.4K]2 months ago

5 0

Answer:

96

Step-by-step explanation:

The highest height achieved by the pebble represented by the quadratic function

$h(t)=-16t^2+32t+80$ can be determined by finding the vertex.

First, we identify the t-coordinate of this vertex. This maximum height corresponds to this value of t, thus, we need to evaluate the h(t)-coordinate.

By comparing $h$ and $at^2+bt+c$ , we observe that:

$a=-16$

$b=32$

$c=80$

Next, we compute to uncover the t-coordinate of the vertex:

$t=\frac{-b}{2a}$

$t=\frac{-32}{2(-16)}$

$t=\frac{-32}{-32}$

$t=1$

Now, substituting t into $-16t^2+32t+80$ with 1 will enable us to find the corresponding h(t)-coordinate:

$-16(1)^2+32(1)+80$

$-16(1)+32+80$

$-16+32+80$

$16+80$

$96$

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