Appendix
A-9: Graphing
Example A-9.6
Create an animation showing how the number and location of the real zeros of the quadratic polynomial x2+b x+3 vary with the parameter b.
Solution
Solution via the Plot Builder in the Context Panel:
Write the quadratic.
Context Panel: Plot Builder animation 2-D plot Change animation parameter from x to b view: axis[2] -25 to 30 build animation
Click on the graph to access the animation toolbar.
x2+b x+3→
There are several other ways to obtain the animation in Figure A-9.6(a). These are explained below.
Options in the animation toolbar are explained in Table 6.5 in the User Manual.
Figure A-9.6(a) Requisite animation
With the syntax shown below, the animate command from the plots package will generate the required animation. The second argument in the animate command is a list of the arguments for the plot command to draw one frame with one value of b.
A much better alternative is the interactive command (in the plots package), which launches the Interactive Plot Builder, allowing for an interactive construction of the animation. (Change the command to Executable before selecting Evaluate from the Context Panel.)
plots:-interactivex2+b x+3
The details of how to implement the animation are as follows.
In the "Select Plot Type and Functions" drop-down, select "Animation." Let b be the animation parameter, but set −10≤b≤10. See Figure A-9.6(b).
In the Options pane, set Range from/to to the interval −25,30. See Figure A-9.6(c).
Press the Preview button to see a preview in a pop-up, and/or press the Plot button to embed the animation into the worksheet.
Figure A-9.6(b) Initial pane in Interactive Plot Builder
Figure A-9.6(c) Top part of Options pane in Interactive Plot Builder
If, instead of selecting "Animation," the choice is "Interactive Plot with 1 parameter," then the Preview button will launch a pop-up Maplet in which a slider controls the parameter b. Pressing the Plot button embeds into the worksheet a slider-controlled graph that is essentially created (behind the scenes) with the Explore command. The embedded graph is, in effect, generated by the following command.
Exploreplotx2+b x+3,x=−10..10,y=−25..30,b=−10..10
b
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