Question

The graph below shows a company's profit f(x), in dollars, depending on the price of erasers x, in dollars, being sold by the company:

graph of quadratic function f of x having x intercepts at ordered pairs 0, 0 and 8, 0. The vertex is at 4, 270

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 = 1 to x = 4, and what does this rate represent? (4 points)

Answer 1

The x-intercepts are the ordered pairs (x, 0).

Since we are graphing (price of erasers, profit), the x-intercepts represent the price of erasers in which the company will profit nothing.

Answer 2

The two ordered pairs are (0, 0) and (8, 0).

*Remember, we are graphing ( Price of Erasers, Profit ).

So when Price of Erasers are 0 and 8, the Profit will be none.

Answer 3

okay and the max is the max profit right?

Answer 4

The vertex is the highest point on the graph. The vertex is (4, 270).

*Remember, it is (Price of Eraser , Profit) :

So when erasers are sold at a price of 4, the Profit is 270.

**It is noteworthy that this means no other eraser price other than 4 will produce as great a Profit.

Answer 5

I see, so as for part A i would write that the x intercepts and maximum of the graph would represent the price of erasers and they only see a maximum profit of $270 when the erasers are priced at $4. Correct @UC66 ?

Answer 6

The x-intercepts are special, the two x-intercepts represent the eraser prices which will grant no Profit.

The maximum of the graph is special, it represents the Eraser Price which will grant greatest Profit.

Answer 7

oh ok i see. So what about "where the function is increasing and decreasing, and what do they represent about the sale and profit?"