To model the motion of a ball dropped from a height of 16 feet, we should look for points that represent the height of the ball at specific times.
From the options provided:
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(0,0) and (1,0) - These points represent no height at the start and at time 1 second, which does not relate to the drop from 16 feet.
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(16,0), (12,0.5), and (0,1) - This option contains a point that doesn't reflect the height of the ball accurately, as it seems to consider 0.5 seconds instead of using increasing times.
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(0,16), (0.5,12), and (1,0) - This set of points indicates that at time 0 seconds, the height is 16 feet (when the ball is released), at 0.5 seconds, the height is 12 feet (the ball has dropped), and finally at 1 second, the height is 0 feet (the ball has hit the ground).
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(0,16), (0.375,14), and (1,0) - This option also begins with the height of 16 feet at time 0 seconds and records a 14 feet height at 0.375 seconds, with the ball reaching 0 feet (ground level) at 1 second.
Between options 3 and 4, both appear to be valid, but option 3 gives a more standard set of intervals (0 seconds, 0.5 seconds, and then 1 second).
Thus, the best answer to find the quadratic equation that models the graph is:
(0,16), (0.5,12), and (1,0).