Final answer:
The average rate of change for the height of the ball from 0 seconds to 2 seconds is 1 unit per second.
Step-by-step explanation:
To find the average rate of change for the height of the ball from 0 seconds to 2 seconds, we need to find the height of the ball at both 0 seconds and 2 seconds, and then calculate the change in height divided by the change in time.
Using the equation H(t) = -(t)^2 + 5t + 8, we can substitute t = 0 and t = 2 to find the heights of the ball at those times. When t = 0, H(0) = -(0)^2 + 5(0) + 8 = 8. When t = 2, H(2) = -(2)^2 + 5(2) + 8 = 10.
The change in height is 10 - 8 = 2, and the change in time is 2 - 0 = 2. Therefore, the average rate of change for the height of the ball from 0 seconds to 2 seconds is 2/2 = 1. The height of the ball increases at an average rate of 1 unit per second during this time interval.