Final answer:
The ball is kicked at time x=0 seconds, and it hits the ground after 2 seconds, as determined by the equation y=-16x²+32x, which gives the height of the ball after x seconds. The correct answer is c. 2s.
Step-by-step explanation:
The equation y=-16x²+32x describes the height (y) of a ball in feet at x seconds after being kicked, assuming no air resistance and that the ball is kicked from ground level. To determine when the ball is kicked and when it hits the ground using a graph, we must find when the height is zero.
At the time of being kicked (x=0), the height equation gives us y=-16(0)²+32(0) = 0. This confirms the ball is at height zero and thus being kicked at time x=0, which corresponds to option (a) 0s.
The ball will hit the ground when y=0 again, but for x > 0. Factoring the equation or finding the roots of the quadratic by setting it equal to zero yields two solutions: x=0 (already discussed) and x=2.
Factoring:
0 = -16x² + 32x
0 = 16x(x - 2)
x = 0 or x = 2
Therefore, the ball hits the ground after 2 seconds, which is option (c) 2s.