Section 6. Explore how the graphs of formulas change as the parameters change.
Example 20. Consider this formula , which is a generalization of the formula we have graphed in several examples in this topic. That example is, so there , , and . In this section, we will use the spreadsheet to graph this in a way that will make it easy to explore what happens when we change one or more of (which we call parameters.)
Setting up the spreadsheet:
- We will graph this for values of x from -6 to +6. So put the label x in cell A1 and then start in A2 with these values and continue through A14.
- Instead of putting the formula directly into column B, we will enter the three initial values , , and in cells over to the side. Please put the values in column G, cells G2, G3, and G4, respectively and the labels in column H.
- Label column B as y. That is, enter y into cell B1. Then enter the formula in cell B2. Notice that the cell references for a, h, and k must be entered with absolute references, so the formula that would have been =2*(A2-3)^2+4 is, instead =$G$2*(A2-$G$3)^2+$G$4
- When this is entered correctly, the numerical value will be 166.
- After the formula is entered correctly, then copy and paste it into the remainder of the cells in column B, which is through B14.
- Then select the data, with the labels. Highlight it. Then choose Insert > Chart and XY Scatter. Choose one of the options that connects the data with curves. Then keep clicking on “Next” until you click on “Finish.” This will produce a graph of the formula with the given values in it.
- Mathematics for Modeling. Authored by: Mary Parker and Hunter Ellinger. License: CC BY: Attribution