Question

3. [09.01] A soccer ball is kicked toward the goal. The height of the ball is modeled by the function h(t) = −16t2 + 48t where t equals the time in seconds and h(t) represents the height of the ball at time t seconds. What is the axis of symmetry, and what does it represent? (2 points) t = 1.5; it takes 1.5 seconds to reach the maximum height and 3 seconds to fall back to the ground t = 1.5; it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground t = 3; it takes 3 seconds to reach the maximum height and 3 seconds to fall back to the ground t = 3; it takes 3 seconds to reach the maximum height and 6 seconds to fall back to the ground

Answer 1

t = 1.5; it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground

Explanation:

The axis of symmetry of a parabola is halfway between the zeros.

h(t) = -16t² + 48t

0 = -16t² + 48t

0 = -16t (t − 3)

t = 0, t = 3

The zeros are t = 0 and t = 3, so the axis of symmetry is t = 1.5. That means it takes 1.5 seconds to reach the maximum height and another 1.5 seconds to return to the ground.