1. The function H= -16T^2+80T+5 is a parabola of the form 
, so to find the maximum height of the ball, we are going to find the y-coordinate of the vertex of the parabola. To find the y-coordinate of the vertex we are going to evaluate the function at the point 
.
From our function we can infer that
and 
, so the point \frac{-b}{2a} [/tex] will be 
. Lets evaluate the function at that point:
We can conclude that the ball reaches a maximum height of 105 feet.
2. Since we now know that the maximum height the ball reaches is 105 feet, we are going to replace
with 105 in our function, then we are going to solve for 
to find how long the ball takes to reach its maximum height:
We can conclude that the ball reaches its maximum height in 2.5 seconds.
3. Just like before, we are going to replace with 5 in our original function, then we are going to solve for to find how long will take for the ball to be caught 5 feet off the ground:
We can conclude that it takes 5 seconds for the ball to be caught 5 feet off the ground.
From our function we can infer that
We can conclude that the ball reaches a maximum height of 105 feet.
2. Since we now know that the maximum height the ball reaches is 105 feet, we are going to replace
We can conclude that the ball reaches its maximum height in 2.5 seconds.
3. Just like before, we are going to replace
We can conclude that it takes 5 seconds for the ball to be caught 5 feet off the ground.