For students in senior secondary school or university courses the use of two variable regression may be an appropriate way to construct a function model for the TotalCost curve. The Spreadsheet View in GeoGebra provides the necessary tools.

Follow the steps below starting with the applet in the worksheet.

1. Drag the purple point along the shoreline to trace out the TotalCost curve and insert values in columns A and B of the Spreadsheet.

2. Select the values in columns A and B of the Spreadsheet by holding the Shift key and clicking on the column labels.

3. Click on the Analysis tool icon and select Two Variable Regression Analysis

4. The regression model window will open. For Regression Model select Polynomial and select degree 2

GeoGebra will apply regression and report a function model and plot the graph (both in red)

5. To use this model further we need to port it to the other windows using the Copy to Graphics View tool

6. Open the Algebra View. We now have the regression model as the curve and the function, g(x).

7. Students can use the function g(x) and their algebra skills to factor the polynomial and locate the vertex.