Final answer:
The domain of the function h(t) = -16t^2 + 40t, for the height of a kicked ball, is the set of non-negative real numbers because time starts at t = 0 and the ball lands after 4 seconds, making option C) the correct answer.
Step-by-step explanation:
The domain of the function h(t) = -16t^2 + 40t, representing the height of a kicked ball, refers to the set of all possible values of time (t) for which the function is defined. Since we cannot have negative time values in this physical context, the domain doesn't include negative numbers. Time starts at t = 0, which is when the ball is released, and it ends when the ball hits the ground. The positive root t = 4.0 s of the quadratic equation suggests that the ball will land after 4 seconds. Therefore, the domain of the function h(t) in this situation is the set of non-negative real numbers, as time cannot be negative and it makes no sense to consider values after the ball has landed.
Option C) Non-negative real numbers is the correct answer.