Answer:
A. The maximum heigh is 81 feet
B. The ball will reach the maximum heiight at 2.25 seconds
C. The domain of the function is ![t\in [0,4.5]](https://tex.z-dn.net/?f=t%5Cin%20%5B0%2C4.5%5D)
D. The range of the function is ![h(t)\in [0,81]](https://tex.z-dn.net/?f=h%28t%29%5Cin%20%5B0%2C81%5D)
E. 4.5 seconds
Step-by-step explanation:
A ball was thrown into the air with an initial velocity of 72 feet per second. The height of the ball after t seconds is represented by the equation:

The maximum height will be at parabola's vertex. Find it:

A. The maximum heigh is 81 feet
B. The ball will reach the maximum heiight at 2.25 seconds
C. Find where the parabola intersects the x-axis:

So, the domain of the function is ![t\in [0,4.5]](https://tex.z-dn.net/?f=t%5Cin%20%5B0%2C4.5%5D)
D. The range of the function is
![h(t)\in [0,81]](https://tex.z-dn.net/?f=h%28t%29%5Cin%20%5B0%2C81%5D)
E. The ball is at the air for 4.5 seconds