Another Parametric on the TI-86

The problem of graphing the parametric equations

x =	t³ – 8	; y =	t³ + 8

	2t²		2t²

is taken from the Precalculus textbook.

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 fifth line and second to move the highlight over to the Param option. At that point we can press to make the 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 graph screen and the graph menu. Then, opens the E(t)= screen. At that point the two parametric equations can be entered.

Figure 4 Before actually moving to the graph, we use the and keys to return to the the graph menu and then to shift that menu so that the FORMT option is visible. Then, pressing opens the FORMAT screen shown in Figure 5.

Figure 5 Note that the calculator used here has the "DrawDot" option set.

Figure 6 To move to Figure 6, press the key to change the menu at the bottom of the screen to the ZOOM menu. Then, press to select the ZSTD settings, and generate a graph.

Figure 7 Figure 7 presents the graph of the parametric equations. However, that graph is vastly different from the one given in the text.

Figure 8 In Figure 8 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 6.28318530718. We will change those values.

Figure 9 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 10.

Figure 10 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 11 opens the FORMAT menu. Here we can change the setting to "DrawLine". Then pressing will cause the calculator to produce the graph shown in Figure 12.

Figure 12 In Figure 12 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 13 We press to return to the E(t)= 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 14.

Figure 14 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 fifth line and second to move the highlight over to the Param option. At that point we can press to make the 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 graph screen and the graph menu. Then, opens the E(t)= screen. At that point the two parametric equations can be entered.
Figure 4	Before actually moving to the graph, we use the and keys to return to the the graph menu and then to shift that menu so that the FORMT option is visible. Then, pressing opens the FORMAT screen shown in Figure 5.
Figure 5	Note that the calculator used here has the "DrawDot" option set.
Figure 6	To move to Figure 6, press the key to change the menu at the bottom of the screen to the ZOOM menu. Then, press to select the ZSTD settings, and generate a graph.
Figure 7	Figure 7 presents the graph of the parametric equations. However, that graph is vastly different from the one given in the text.
Figure 8	In Figure 8 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 6.28318530718. We will change those values.
Figure 9	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 10.
Figure 10	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 11	opens the FORMAT menu. Here we can change the setting to "DrawLine". Then pressing will cause the calculator to produce the graph shown in Figure 12.
Figure 12	In Figure 12 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 13	We press to return to the E(t)= 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 14.
Figure 14	The two new relations appear on Figure 14.