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
There are several ways to obtain the animation in Figure A-9.6(a). These are explained below.
Click on the graph to access the animation toolbar.
Options in the animation toolbar are explained in Table 6.5 in the User Manual.
Figure A-9.6(a) Requisite animation
Animation via Plot Builder
Enter the polynomial.
Context Panel: Plot Builder≻animation
2-D plot
In the animation section, set b as the animation parameter and set its range as −10,10.
Set −10≤x≤10.
view: axis[2]≻−25,30
Click the "build animation" button
x2+b x+3→
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 Plot Builder, allowing for an interactive construction of the animation.
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 Plot Builder
Figure A-9.6(c) Top part of Options pane in 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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