To model the height of a ball being dropped from a height of 16 feet, we need to focus on key points that represent the scenario.
- The ball starts at a height of 16 feet when time \( t = 0 \). So, the point \( (0, 16) \) is important.
- The ball eventually hits the ground, which means it reaches a height of 0 feet. This occurs at some point in time, and typically for a ball dropped from 16 feet, it would reach the ground at 1 second, so the point \( (1, 0) \) is also needed.
- The height of the ball decreases as time increases, and the intermediate value at \( t = 0.5 \) seconds would logically be lower than 16 feet, but needs to be checked against the curve.
Given these considerations, the best choice among the options to define points on the curve and derive a quadratic equation would be the first option:
(0,16), (0.5,12), and (1,0)
This option includes:
- Starting height \((0, 16)\)
- Height at an intermediate time \((0.5, 12)\)
- When it reaches the ground \((1, 0)\)
Thus, these points help in finding a quadratic equation that effectively models the graph of the ball's height over time.
So the answer is: (0,16), (0.5,12), and (1,0).