E1.09: Section 6 Part 1

Section 6. Explore how the graphs of formulas change as the parameters change.

Example 20.   Consider this formula [latex]y=a{{(x-h)}^{2}}+k[/latex], which is a generalization of the formula we have graphed in several examples in this topic. That example is[latex]y=4+2{{(x-3)}^{2}}=2{{(x-3)}^{2}}+4[/latex], so there [latex]a=2[/latex], [latex]h=3[/latex], and [latex]k=4[/latex]. 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:

  1. 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.
  2. Instead of putting the formula directly into column B, we will enter the three initial values [latex]a=2[/latex], [latex]h=3[/latex], and [latex]k=4[/latex] 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.
  3. 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
  4. When this is entered correctly, the numerical value will be 166.
  5. After the formula is entered correctly, then copy and paste it into the remainder of the cells in column B, which is through B14.
  6. 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.
  A B C D E F G H
1 x y
2 -6 166 2 a
3 -5 132 3 h
4 -4 102 4 k
5 -3 76
6 -2 54
7 -1 36
8 0 22
9 1 12
10 2 6
11 3 4
12 4 6
13 5 12
14 6 22