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 = 22 to x = 26, and what does this rate represent? (4 points

the complete question in the attached figure

part A

the x intercept 0 is the point where the ball was hit, the x intercept 20 is the point where the ball fell back to the ground, 20 feet away from the kicker.

the function is increasing in the interval x∈(0, 10) and decreasing in x∈(10, 20) 
this means that the height is increasing in the interval  (0, 10) and decreasing as x goes through the interval (10,20)
the distance from the kicker is increasing during the whole interval (0, 20)

part B

the rate of change represents the slope of the secant line from A to B. It approximates the rate at which f(x) decreases or increases in the interval 

x =[A, B]

a negative exponent is translated as follows:

so, we have

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!