4. A basketball player has a jump shot that moves in a parabolic arc. When she
released the basketball at a recent game, the ball was 10 ft vertically off the
ground and 20.25 ft horizontally from the center of the basket. The ball reached
its maximum height of 14 ft when it was 12.375 ft horizontally from the center of
the hoop. Unfortunately, when the ball returned to a height of 10 ft, it did not go
through the hoop. The diameter of the hoop is 18 in., and the hoop is connected
to the backboard by a 6-in. bracket.
(a)
Using values relative to the location on the floor directly under the
backboard, make a table of values that relates the horizontal distance of the
basketball from the backboard to its vertical distance above the ground.
(b) Determine a quadratic regression equation for your data. Explain why a
quadratic model is appropriate for this scenario.
