Pl helppp im marking brainlies i swear
The graph below shows a company's profit f(x), in dollars, depending on the price of pencils x, in dollars, sold by the company:

Graph of quadratic function f of x having x intercepts at ordered pairs negative 0, 0 and 10, 0. The vertex is at 5, 160.

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 sale and profit? (4 points)

Part B: What is an approximate average rate of change of the graph from x = 2 to x = 5, and what does this rate represent? (3 points)

Part C: Describe the constraints of the domain. (3 points)

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 sale and profit?

Let

x > the price of pencils in dollars

f(x) > a company's profit in dollars

we know that

The function f(x) is a quadratic function having x-intercepts at (0,0) and (10,0)

The x intercepts give us the price when profit is zero, so the x-intercepts represent break-even points

The vertex is at (5,160)

f(x) represent a vertical parabola open downward

The vertex is a maximum

The x-coordinate of the vertex represent the price of the pencils when the value of the profit is maximum

The y-coordinate of the vertex represent the maximum profit

therefore

The maximum profit of $160 is when the price of the pencils is $5

Profit is increasing on the interval (0,5) and decreasing on the interval (5,10)

This represents that profit is increasing when selling price ranges from 0 dollars to 5 dollars, then decreases when selling price is 5 dollars to 10 dollars

B.  What is an approximate average rate of change of the graph from x = 2 to x = 5, and what does this rate represent?

Find the average rate of change of the graph from x = 2 to x = 5

To find the average rate of change, we divide the change in the output value by the change in the input value

the average rate of change using the graph is equal to

In this problem we have

Looking at the graph

Substitute

The average rate of change from x=2 to x=5 is 20.

This tells us there is a 20 dollar increase in profit for each dollar increase in selling price for prices between 2 and 5 dollars