Chapter 8.4A, Problem 19A

A ball is shot out of a cannon at ground level. Its height H in feet after t sec is given by the function $H\left(t\right)=128t-16t^2$.

a. Find $H\left(2\right),H\left(6\right),H\left(3\right),\text{and }H\left(5\right)$. Why are some of the outputs equal?

b. Graph the function and from the graph find at what instant the ball is at its highest point. What is its height at that instant?

c. How long does it take for the ball to hit the ground?

d. What is the domain of H?

e. What is the range of H?