Using the TI-83/84 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 = t2 3

with -3 ≤ t ≤ 3

Notice X1T and Y1T.

Set the WINDOW for t as indicated.

The x-values would be -1.5 to 1.5 because x = 0.5t. The y-values would be -3 to 5 because y = t2 3. We set the window slightly larger than the minimum.

Convert the parametric equations x = 0.5t

y = t2 3

-3 ≤ t ≤ 3

into rectangular equations.


Solve x = 0.5t for t = 2x and substitute into

y = t2 3 to get

y = (2x)2 3 or

y = 4x2 3 in rectangular form.

Press Y= and enter

Y1 = 4x2 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 = x2 - 1.

Let x = t. Then

y = t2 1.

Tstep=1 for graph on left.


Tstep=.1 for graph on right.