Final answer:
The statement about the soccer ball reaching the ground when the quadratic function value is zero is true. Solving the quadratic equation of the ball's projectile motion gives us the time when the ball hits the ground; only the positive value is physically meaningful.
Step-by-step explanation:
When a soccer ball is kicked into the air, the ball will continue to rise until gravity slows it down to a stop, after which the ball will fall back to the ground. The scenario described can be analyzed using a quadratic function that models projectile motion. The statement given is true; to find the time the ball takes to hit the ground, we must set the height function to zero (h(t) = 0) because this represents the ball being at ground level. Solving this quadratic equation gives us the time values when the ball is at ground level.
Using the specific function h(t) = -16t2 + 32t, we'd find the times when the ball is on the ground by setting h(t) to zero and solving for t. We get two solutions because the ball crosses the ground level twice, once on the way up (which results in a negative time and is not physically meaningful in this context) and once on the way down. The positive solution represents the time after the kick when the ball hits the ground. Therefore, to find out how long it remains in the air, we take the positive root from the solutions obtained from the quadratic formula or by factoring if possible.