Super Jay, a large supermarket chain, conducted a market analysis on their store brand of flake breakfast cereal. The chain set various prices for its 500g box at various stores. The Super Jay researchers tracked the weekly sales for each price. The data they obtained is shown in the table below. Determine the equation of a polynomial function that best models this data.

Price per box ($)
Boxes sold
38 320
33 710
28 280
26 550
25 530
22 170
18 260

Step 1: Turn on the STAT PLOT; press 2nd, Y=, ENTER, ENTER.

Step 2: Clear the functions; press Y= then, CLEAR for each function that needs deleting.

Step 3: Select values for the viewing window; press WINDOW.

Step 4: Go to the lists; press STAT, ENTER.

Step 5: Clear the lists; press the up arrow until the column heading is highlighted then, CLEAR, ENTER. Repeat for all columns that have unneeded data.

Step 6: Enter the data. (L1 = Price per box; L2 = Boxes sold.)

Step 7: View the data; press GRAPH.

Step 8: Choose the regression model; press STAT, right arrow.

Step 9: Select the cubic regression; press 6.

Step 10: Place the cubic regression into the function area; press VARS, right arrow, ENTER, ENTER, ENTER.

Step 11: View the scatter plot and regression model; press GRAPH.

In standard form, the cubic regression, rounded to the nearest whole number, is as follows:

y = −20035x3 + 184857x2 − 577955x + 637905