Question

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.

Answer 1

Answer:

96

Step-by-step explanation:

The maximum height reached by the pebble modeled by the quadratic function,

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

Let's first find the t-coordinate of the vertex . The max height will correspond to this value of t which means we have to find the h(t)-coordinate.

When comparing $h$ to $at^2+bt+c$, we see that:

$a=-16$

$b=32$

$c=80$

We need to evaluate the following to find the t-coordinate of the vertex:

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

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

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

$t=1$

So now to find the correspond h(t)-coordinate, we will need to replace t in $-16t^2+32t+80$ with 1:

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

$-16(1)+32+80$

$-16+32+80$

$16+80$

$96$