So first we must know that the function is a quadratic. And that the maximum exists. It is also important to know that the maximum height will occur when the velocity equals zero. So, knowing that, we must derive the height function to find the velocity in terms of time.
This comes out to be:
velocity = -32t + 28
Then we set velocity as zero to find the time at which the ball reaches its highest point.
0 = -32t + 28
t = 0.736
Now that we have the time, you can answer the first question. The ball reaches its maximum height after 0.736 seconds. To answer the second question, you can substitute this back into the height formula.
h = -16(0.736)^2 + 28(0.736) +7
h = 18.938
Therefore the maximum height is 18.938 ft.
