Please help with this, will give brainliest. The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, being sold by the company:

graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 6, 0. The vertex is at 3, 120

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? (6 points)

Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent? (4 points)

(10 points)

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  A. x-intercepts: prices at with profit is zero

     maximum: price at which profit is a maximum

     increasing: (-∞, 3); decreasing: (3, ∞) — profit increases with increasing pen price below $3, decreases with increasing pen price above $3

  B. -26 2/3; loss of profit for each dollar increase in pen price

Step-by-step explanation:

Part A:

The definition of the function tells you what points on the graph represent. The x-intercept at x=0 tells you the company's profit will be zero when the price of pens sold by the company is zero.

The x-intercept at x=6 tells you the company's profit will be zero when the price of pens sold is $6.

The maximum value of 120 at x=3 tells you the company's profit will be $120 when the price of pens sold is $3.

The graph goes "uphill" for x < 3, so the function is increasing for x < 3. The function goes "downhill", so is decreasing, for x > 3. This tells you profit increases with pen price when the price is below $3, and decreases with pen price above $3.

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Part B:

The equation of the function describing the graph is ...

  f(x) = -120/9x(x -6)

so, at x=5, the value is ...

  f(5) = -120/9(5)(-1) = 600/9 = 66 2/3

Then the average rate of change from x=3 to x=5 is ...

  m = (f(5) -f(3))/(5 -3) = (66 2/3 -120)/2 = (-53 1/3)/2 = -26 2/3

This represents the average change in profit for each dollar increase in the price at which pens are sold.

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step-by-step explanation:

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