Question

A football is kicked toward the goal. The height of the ball is modeled by the function h(t) = -16t2 + 64t where t equals the time in seconds and h(x) represents the height of the ball at time t seconds. What is the axis of symmetry and what does it represent?

t = 2; it takes 2 seconds to reach the maximum height and 2 seconds to fall back to the ground
t = 2; it takes 2 seconds to reach the maximum height and 4 seconds to fall back to the ground
t = 4; it takes 4 seconds to reach the maximum height and 4 seconds to fall back to the ground
t = 4; it takes 4 seconds to reach the maximum height and 8 seconds to fall back to the ground

Answer 1

Answer: B/ it takes 2 seconds to reach the maximum height and 4 seconds to fall back to the ground

Explanation:

Answer 2

h(t) = -16(t^2) + 64t

roots:

0 = -16t^2 + 64t
0 = t^2 - 4t
0 = t(t-4)
t=0 and t =4

The symmetry axis is at the middle of the two roots: t = (0+4)/2

That time (t=2) is what it takes the object to reach the maximum height.

Answer: t = 2; it takes 2 seconds to reach the maximum height and 4 seconds to fall back to the ground