Firstly, press [MODE] and select Graph.....PARAMETRIC

In the Y= screen, enter the parametric equations:
xt1 = 1 - t²   ;   yt1 = 2t - 4

To set up the split screen, press [MODE] and in Page 2 set:

From the GRAPH screen, press [¨][WINDOW] and set the following scale for the axes:

and then press [¨][GRAPH] to display the graph.

Now move across by [2nd][APPS] to the TABLE screen. Press [¨][TblSet] and enter the values tblStart: -3 and delta-tbl: 0.5. Also, press [F1] 9:Format and select Cell Width = 5

Your screen should look like:

Moving back to the GRAPH screen, press [F3 Trace]. The flashing cursor appears at one end of the curve, and the (t,x,y) coordinates are shown at the bottom of the screen. Pressing the cursorpad right or left moves the cursor along the graph in t-increments of 0.5, in keeping with the table of values alongside. This provides the individual frames for the animation. When you arrive at the point where t=0, move across to the TABLE screen and scroll down to display the set of coordinates from t = 0 to 3.

Use the TI-GRAPHLINK to capture each screenshot, copy each image into a graphics software package to save as a .gif file, and use these individual images with your chosen GIF Animation programme.