The graph of the function f(t)= -16t^2 + 100t. The independent variable is time in seconds and the dependent is hieght in feet. The domain is all real numbers and the range is
y<\= 156.25. The ball is in the air for 6.25 seconds.
The maximum height of the ball is about 156 feet. It takes about 3 seconds for the ball to reach the maximum height. The height of the ball at 3.5 seconds is 154 feet. Also at 2.75, the ball is at 154 feet. At about 5.5 seconds, it is at 65, as you can see on the graph.
Gloria and Earl
The function of Gloria is f(t)=-16t^2+80t. For Earl, his function is f(t)=-16t^2+100t. Gloria's ball will hit the ground before Earl's. Her ball hits at 1.25 seconds sooner than his. Gloria's ball went 100 feet. Earl's ball went 56.25 feet more than Gloria's ball went.
Earl plus 20
Supposing that Earl hit a second ball at 20 more feet than the other one, it would effect the elevation by making the vertex greater. The function of the second ball would be f(t)=-16t^2+120t. The domain is all real numbers and the range is y<\= 225.
Tweety Bird hits ball at the same time and tee that I did. His height was increasing at 4 feet per second. He will be at the same height as my ball at 6 seconds. That height will be 24 feet.