Question

A football is kicked toward the goal. The height of the ball is modeled by the function h(x) = -16t^2 + 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?

A. x = 2; it takes 2 seconds to reach the maximum height and 2 seconds to fall back to the ground

B. x = 2; it takes 2 seconds to reach the maximum height and 4 seconds to fall back to the ground

C. x = 4; it takes 4 seconds to reach the maximum height and 4 seconds to fall back to the ground

D. x = 4; it takes 4 seconds to reach the maximum height and 8 seconds to fall back to the ground

Answer 1

A

Explanation:

Answer 2

We will solve the equation:
`-16 x^(2) +64t=0`
t(-16 t + 64 )=0, t1=0,
-16t+64=0, 16 t = 64, t2=4
This is a square function ( graph : parabola ) with the zeroes: t1=0 and t2=4.
The axis of symmetry is x=2. It takes 2 seconds to reach the maximum height and 2 seconds to fall back to the ground (Answer: A).