Using the
TI83/84 Calculators to Graph Parametric Equations 

In order to graph parametric equations, set the MODE for PAR by pressing the MODE button and the down arrow to highlight PAR for parametric. 
Graph the parametric equations x = 0.5t y = t^{2} – 3 with 3 ≤ t ≤ 3 Notice X_{1T} and Y_{1T}. 

Set the WINDOW for t as indicated. The xvalues would be 1.5 to 1.5 because x = 0.5t. The yvalues would be 3 to 5 because y = t^{2} – 3. We set the window slightly larger than the minimum. 
Convert the parametric equations x = 0.5t y = t^{2} – 3 3 ≤ t ≤ 3 into rectangular equations. 


Solve x = 0.5t for t = 2x and substitute into y = t^{2} – 3 to get y = (2x)^{2} – 3 or y = 4x^{2} – 3 in rectangular form. 
Press Y= and enter Y1 = 4x^{2} – 3 with the window set as indicated on the left. We see that the parametric and rectangular graphs are the same. 

Find a set of parametric equations for the rectangular equation: y = x^{2}  1. Let x = t. Then y = t^{2} – 1. 
Tstep=1 for graph on left.
Tstep=.1 for graph on right. 