# How to Graph Parametric Equations on the TI-83 Plus

After you have entered the parametric equations into the TI-83 Plus graphing calculator, you can use the following steps to graph the equations:

1. Turn off any Stat Plots that you don’t want to appear in the graph of your parametric equations.

The first line in the Y= editor tells you the graphing status of the Stat Plots.

If Plot1, Plot2, or Plot3 is highlighted, then that Stat Plot will be graphed along with the graph of your parametric equations. If it’s not highlighted, it won’t be graphed.

To turn off a highlighted Stat Plot in the Y= editor, use the

keys to place the cursor on the highlighted Stat Plot and then press [ENTER]. The same process is used to rehighlight the Stat Plot in order to graph it at a later time.

When graphing parametric equations, Stat Plots that are turned on when you don’t really want them to be graphed cause problems. The most common problem is the ERR: INVALID DIM error message. This error message gives you little insight into what is causing the problem. So if you aren’t planning to graph a Stat Plot along with your parametric equations, please make sure all Stat Plots are turned off.

2. Press [2nd][ZOOM] to access the Format menu.

3. Set the format for the graph by using the

keys to place the cursor on the desired format and then press [ENTER].

The first line of the Format menu when the calculator is in Parametric mode gives you a choice between having points on the graph displayed in rectangular form or in polar form. When graphing parametric equations, there is no harm in leaving these items highlighted.

4. Press [WINDOW] to access the Window editor.

5. After each of the first three window variables, enter a numerical value that is appropriate for the parametric equations you’re graphing. Press [ENTER] after entering each number.

If you know the dimensions of the viewing window required for your graph, go ahead and assign numerical values to the remaining variables in the Window editor and advance to Step 8. If you don’t know the minimum and maximum x and y values required for you graph, the next step tells you how to get the calculator to find them for you.

6. Press [ZOOM][0] to access ZoomFit.

After you’ve assigned values to Tmin, Tmax, and Tstep, ZoomFit determines appropriate values for Xmin, Xmax, Ymin, and Ymax, and then graphs your parametric equations. Note, however, that ZoomFit graphs parametric equations in the smallest possible viewing window, and it doesn’t assign new values to Xscl and Yscl.

If you like the way the graph looks, then you can skip the remaining steps. If you’d like spruce up the graph, Step 7 gives you some pointers.

7. Press [WINDOW] and adjust the values assigned to the X and Y settings. Press [ENTER] after entering each new number.

Here are some pointers on how to readjust the viewing window after using ZoomFit:

• Xmin and Xmax: If you don’t want the graph to hit the left and right sides of the screen, decrease the value assigned to Xmin and increase the value assigned to Xmax. If you want to see the y-axis on the graph, assign values to Xmin and Xmax so that zero is strictly between these two values.

• Xscl: Set this equal to a value that doesn’t make the x-axis look like railroad tracks — that is, an axis with far too many tick marks. Twenty or fewer tick marks makes for a nice looking axis.

• Ymin and Ymax: If you don’t want the graph to hit the top and bottom of the screen, decrease the value assigned to Ymin and increase the value assigned to Ymax. If you want to see the x-axis on the graph, assign values to Ymin and Ymax so that zero is strictly between these two values.

• Yscl: Set this equal to a value that doesn’t make the y-axis look like railroad tracks. Fifteen or fewer tick marks is a nice number for the y-axis.

8. Press [GRAPH] to regraph the parametric equations.

After you’ve graphed your parametric equations, you can draw lines and functions on the graph or write text on the graph. And you can save a picture of the graph and the drawings.