Answer:
96
Step-by-step explanation:
The maximum height reached by the pebble modeled by the quadratic function,
[tex]h(t)=-16t^2+32t+80[/tex], 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 [tex]h[/tex] to [tex]at^2+bt+c[/tex], we see that:
[tex]a=-16[/tex]
[tex]b=32[/tex]
[tex]c=80[/tex]
We need to evaluate the following to find the t-coordinate of the vertex:
[tex]t=\frac{-b}{2a}[/tex]
[tex]t=\frac{-32}{2(-16)}[/tex]
[tex]t=\frac{-32}{-32}[/tex]
[tex]t=1[/tex]
So now to find the correspond h(t)-coordinate, we will need to replace t in [tex]-16t^2+32t+80[/tex] with 1:
[tex]-16(1)^2+32(1)+80[/tex]
[tex]-16(1)+32+80[/tex]
[tex]-16+32+80[/tex]
[tex]16+80[/tex]
[tex]96[/tex]
