The function $h(t)$ outputs the height of a toy rocket measured in feet at time $t$ seconds after it was launched.

$h(t)=-16t^2+128t+2$

a$.$ Calculate the height of the rocket at time $2$ seconds after launch.

$h(2)=-16(2{)}^2+28(2)+2$

$=-64+256+2$

$=194$ feet

b$.$ Calculate the height of the rocket at time $3$ seconds after launch.

$u(3)=-16(3{)}^2+128(3)+2$

$=-144+384+2$

$=242$ feet

c$.$ Calculate the slope of the line that goes through the two points you found in part a anc

$=\frac{242-194}{3-2}=48$

d$.$ What are the units of this slope?

e$.$ What does that slope represent?

How could this be represented on the graph of $h(t)?$