Another Parametric on the TI-83

Note that the TI-83 and the TI-83 plus have slightly different keys. This page uses the keys associated with the TI-83. The differences are that the TI-83 key is replaced by the TI-83 Plus key, and the TI-83 key is replaced by the TI-83 Plus key.

The problem of graphing the parametric equations

x =	t³ – 8	; y =	t³ + 8

	2t²		2t²

is taken from the Precalculus textbook. The solution given in the text uses a TI-86. We will develop the solution for the TI-83.

Figure 1 Pressing opens the screen shown in Figure 1. Here we note that the calculator is currently set in "Function" mode. We will need to change this to "Parametric" mode. To do this we use the cursor keys first to move down to the fourth line and second to move the highlight over to the Par option. We can press to make the setting change here. Then, we can move to the next line, where we place the highlight on "Dot". At that point we can press to make this setting change. This will produce Figure 2.
Figure 2 Now that the setting has been changed, the next step is to enter the parametric equations.

Figure 3 Pressing opens the Y= screen. However, now that we are in PARAMETRIC mode, that screen expects pairs of equations that give parametric expressions first for X_T and then Y_T. At this point we enter the two parametric equations, using the key to enter the parameter T.

Figure 4 To move to Figure 4, press the key to open the ZOOM. Then, press to select the ZStandard settings, and generate a graph.

Figure 5 Figure 5 presents the graph of the parametric equations. However, that graph is vastly different from the one given in the text.

Figure 6 In Figure 6 we use the key to select the WIND option from the menu and to open the WINDOW screen shown. Note that T starts at 0 and increases in relatively small steps until it is greater than 6.2831853... . We will change those values.

Figure 7 Now we will request that T start at ^–10, increase in steps of 0.1, and stop only when it reaches 10. We can press to generate the graph in Figure 8.

Figure 8 Now the graph is starting to look more like the one given in the text. We note that by including negative values for T we have produced a whole new part of the graph. Values of T that are close to zero are sending the relation off to the upper left of the graph.
We can force the calculator to fill in between points by changing the settings.

Figure 9 opens the MODE menu. Here we can change the setting to "Connected". Then pressing will cause the calculator to produce the graph shown in Figure 10.

Figure 10 In Figure 10 the graph of the relation seems essentially identical to the one given in the text. However, the text graph includes the two lines, Y=X and Y=^–X. We can not enter those functions directly on this graph because we are in parametric mode, not function mode. (The lines in the graph in the text were not created on the calculator.) We can, however, create the parametric version of the two lines.

Figure 11 We press to return to the Y= screen. Here we add the parametric equations X=T and Y=T for Y=X X=T and Y=^–T for Y=^–X At that point, will produce the graph in Figure 12.

Figure 12 The two new relations appear on Figure 14.

Figure 1	Pressing opens the screen shown in Figure 1. Here we note that the calculator is currently set in "Function" mode. We will need to change this to "Parametric" mode. To do this we use the cursor keys first to move down to the fourth line and second to move the highlight over to the Par option. We can press to make the setting change here. Then, we can move to the next line, where we place the highlight on "Dot". At that point we can press to make this setting change. This will produce Figure 2.
Figure 2	Now that the setting has been changed, the next step is to enter the parametric equations.
Figure 3	Pressing opens the Y= screen. However, now that we are in PARAMETRIC mode, that screen expects pairs of equations that give parametric expressions first for X_T and then Y_T. At this point we enter the two parametric equations, using the key to enter the parameter T.
Figure 4	To move to Figure 4, press the key to open the ZOOM. Then, press to select the ZStandard settings, and generate a graph.
Figure 5	Figure 5 presents the graph of the parametric equations. However, that graph is vastly different from the one given in the text.
Figure 6	In Figure 6 we use the key to select the WIND option from the menu and to open the WINDOW screen shown. Note that T starts at 0 and increases in relatively small steps until it is greater than 6.2831853... . We will change those values.
Figure 7	Now we will request that T start at ^–10, increase in steps of 0.1, and stop only when it reaches 10. We can press to generate the graph in Figure 8.
Figure 8	Now the graph is starting to look more like the one given in the text. We note that by including negative values for T we have produced a whole new part of the graph. Values of T that are close to zero are sending the relation off to the upper left of the graph. We can force the calculator to fill in between points by changing the settings.
Figure 9	opens the MODE menu. Here we can change the setting to "Connected". Then pressing will cause the calculator to produce the graph shown in Figure 10.
Figure 10	In Figure 10 the graph of the relation seems essentially identical to the one given in the text. However, the text graph includes the two lines, Y=X and Y=^–X. We can not enter those functions directly on this graph because we are in parametric mode, not function mode. (The lines in the graph in the text were not created on the calculator.) We can, however, create the parametric version of the two lines.
Figure 11	We press to return to the Y= screen. Here we add the parametric equations X=T and Y=T for Y=X X=T and Y=^–T for Y=^–X At that point, will produce the graph in Figure 12.
Figure 12	The two new relations appear on Figure 14.