Question

Airplane height, in feet: h = 144Baseball height, in feet: h = 96t - 1612Choose the graph of the system shown above.

Answer 1

Given:

The airplane height

$h=144$

Baseball height is

$h=96t-16t^2$

Find-:

Chose the function graph

Explanation-:

The maximum value of baseball height is

$h=96t-16t^2$

The critical value is

$\begin{gathered} h=96t-16t^2 \\ \\ h^{\prime}=96-16(2)t \\ \\ h^{\prime}=96-32t \end{gathered}$

For the maximum value is h' = 0 is

$\begin{gathered} h^{\prime}=0 \\ \\ 96-32t=0 \\ \\ 32t=96 \\ \\ t=\frac{96}{32} \\ \\ t=3 \end{gathered}$

The maximum value at " t = 3 "

$\begin{gathered} h=96t-16t^2 \\ \\ t=3 \\ \\ h=96(3)-16(3^2) \\ \\ h=96(3)-16(9) \\ \\ h=288-144 \\ \\ h=144 \end{gathered}$

The t² is a negative value so the graph is down open graph

Then the graph is

So, option "C" is the right choose.