Question

(08.01, 08.04 MC)

The graph below shows a company's profit f(x), in dollars, depending on the price of pens x, in dollars, 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? (4 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? (3 points)

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

Answer 1

Answer:

Step-by-step explanation:

Part A:

          The X intercepts represent when the profit is zero. The maximum value  is at the vertex and is where the maximum profit occurs. The function is increasing  until it reaches the vertex and is decreasing after the vertex. The profit is increasing until it reaches its peak at the vertex and is decreasing after the vertex until they reach the zero. Profits are negative to the left of the first zero and to the right of the second zero

(- intinity to 0) negative profit but increasing(0 to 3) increasing profit 3 maximum profit (3 to 6)decreasing profit but still positive (6 to - infinity) decreasing negative profit.

Part B:

          The approximate rate of change is how much the profit decreases when we go from 3 ft height to 5.

f(5) - f(3)

__________

5 - 3

Approximate the values of f(5)- f(3) from your graph.

Part C:

           The domain is constrained by X at=0 we can't sell pay people to take the item. Business wise, we are obliged at X = 6 because we do not want to make a negative profit.

The project code is #SPJ2

Answer 2

Part A:

• The x-intercepts represent a zero profit.
• The maximum value of the graph represents the maximum profit.
• The function increases up till the vertex and decreases after it.
• This means that the profit increases as it reaches the peak at the vertex.
• It decreases after the vertex up till it reaches zero.
• On the left of the first zero and on the right of the second zero, the profits are negative.

Part B:

• An approximate average rate of change of the graph from $x=3$ to $x =5$ represents the reduction in profit from $3$ to $5$.

Part C:

• Simply, the domain is constrained by $x=0$.
• We are obliged at $x=6$.
• This is because we have to avoid a negative profit.

#SPJ2