45 points and !
the graph below shows the height of a kicked soccer ball f(x), in feet, depending on the distance from the kicker x, in feet:

part a: what do the x-intercepts and maximum value of the graph represent? what are the intervals where the function is increasing and decreasing, and what do they represent about the distance and height? (6 points)

part b: what is an approximate average rate of change of the graph from x = 8 to x = 13, and what does this rate represent? (4 points)

PART A:

The x-intercept at 0 shows the location where the ball was kicked. The x-intercept at x = 16 shows the location where the ball hit the ground.

The maximum value represents the highest point of the ball.

The interval where the function is increasing is 0<x<8. Between this interval, the height of the ball measured from the ground is increasing.
The interval where the function is decreasing is 0<x<16. Between this interval, the height of the ball is decreasing.

PART B:

Reading from the graph

When x = 8, y = 10 ⇒ let this be x₁ = 8 and y₁ = 10
When x = 13, y = 6 ⇒ let this be x₂ = 13 and y₂ = 6

The rate of change = (y₂-y₁) / (x₂-x₁)
The rate of change = (6 - 10) / (13 - 8)
The rate of change = -4 / 5 = -(4/5)