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

Good evening.

The simetry axis can be found with the vertex in x formula:



Whe take from the function:

a = -16
b = 48

So:



We can conclude that the axis of simetry is the line with the equation:

t = 3/2

It represents that if we take two points at the same x-distance to this line, they will have the same image(value in h).

For example:

t' = 3/2 + 1/2 = 4/2 = 2
t'' = 3/2 - 1/2 = 2/2 = 1

We calculate h(t):



Where we can se the same h-value.

Doubts? Please, comment :)