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(t) represents the height of the ball at time t seconds. what is the axis of symmetry, and how does it relate to the time the ball is in the air? t = 2; it takes the ball 2 seconds to reach the maximum height and 2 more seconds to fall back to the ground. t = 2; it takes the ball 2 seconds to reach the maximum height and 4 more seconds to fall back to the ground. t = 4; it takes the ball 4 seconds to reach the maximum height and 4 more seconds to fall back to the ground. t = 4; it takes the ball 4 seconds to reach the maximum height and 8 more seconds to fall back to the ground.

Question

contestada

Respuesta :

anjithaka anjithaka · Answer 1 · 2022-08-08T14:34:08+02:00

The function [tex]H(t) = -16t^2 + 64t[/tex] exists in a parabola.

The axis of symmetry of a parabola exists at the midpoint between the two real roots.

The roots exist the solutions of H(t) = 0

To estimate the roots equation exists [tex]-16t^2 + 64t = 0[/tex]

Factor t(-16t + 64) = 0

t = 0 and -16t + 64 =0

-16t + 64 = 0

t = 64 / 16 = 4

t = 4

Then the two roots are t = 0 and t = 4, and the axis of symmetry exists

t = (0+4)/2 = 4/2 = 2

The axis of symmetry exists at t = 2.

It represents the time at which the ball is at the higher point, the maximum height.

You can find the maximum height replacing t = 2 in the function H(t)

[tex]H(t) = -16(2^2) + 64(2)[/tex]

= 64 feet.

And you can also deduce that the second part of the flight will take 2 seconds, for a total flight time of 4 seconds.

To learn more axis of symmetry refers to:

https://brainly.com/question/21191648

#SPJ4