Appendix
A-9: Graphing
Example A-9.7
Explore how the graph of the quadratic polynomial a x2+b x+c depends on each of the parameters a, b, c.
Solution
Interactive Solution
The slider-controlled graph in Figure A-9.7(a) can be obtained by clicking the button .
The tool in Figure A-9.7(a) can be constructed interactively with the by implementing the following steps.
In the "Select Plot Type and Functions" drop-down, select "Interactive Plot with 3 parameters."
Set the range for x and each of the three parameters to the interval −10,10. See Figure A-9.7(b).
In the Options pane, set Range from/to to the interval −25,30 as shown in Figure A-9.7(c). Press the Preview button to obtain the pop-up shown in Figure A-9.7(a) where the three parameters are under the control of sliders, one for each parameter.
Press the Plot button to obtain the embedded animation shown below the discussion of the Explore command. (The embedded animation will be generated internally by that command.)
Figure A-9.7(a) Interactive plot with three parameters
Figure A-9.7(c) Top of Options pane in Plot Builder
Figure A-9.7(b) First pane of Plot Builder
Although the Explore command can be applied through the Context Panel, more control over the resulting graph is possible with a direct invocation of the command itself. This is illustrated below. The result is an embedded tool equivalent to the one described above.
Exploreplota x2+b x+c,x=−10..10,−25..30,parameters=a=−10..10.0,b=−10..10.0,c=−10..10.0,initialvalues=a=1.0,b=1.0,c=1.0
Coded Solution
With the syntax shown below, the interactiveparams command from the plots package will generate the same pop-up with three sliders controlling the values of the parameters a, b, c.
plotsinteractiveparamsplot,a x2+b x+c,x=−10..10,−25..30,a=−10..10,b=−10..10,c=−10..10
Alternatively, use the Explore command as per the following.
Exploreplota x2+b x+c,x=−10..10,−25..30,parameters=a=−10..10.0,b=−10..10.0,c=−10..10.0
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