24.10: E1.09- Section 6 Part 1
- Page ID
- 51752
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)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.
| 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 | ||||||
| 15 |
- Mathematics for Modeling. Authored by: Mary Parker and Hunter Ellinger. License: CC BY: Attribution