Question

On a game show, contestants shoot a foam ball toward a target. The table includes points along one path the ball can take to hit the target where x is the time that has passed since the ball was launched and y is the height at this time.

Time (x)

Height (y)
0 10
2 24
16 10
How high was the ball after 8 seconds?

20 feet
42 feet
96 feet
106 feet

Answer 1

42 feet

Reason: model y = ax^2 + bx + c. From (0,10) c = 10. Using (2,24) and (16,10) gives 2a + b = 7 and 16a + b = 0, so a = -1/2, b = 8. Thus y = -0.5x^2 + 8x + 10 and y(8) = -0.5(64) + 64 + 10 = 42.