Topic: Complex, Parametric, and Polar Forms

Subtopic: Parametric Equations and Graphs

**Overview**

Ready to learn a whole new way to graph? Instead of graphing functions in the form y=f(x), in this lesson we graph parametric equations. __Parametric equations__ are pairs of equations where the x and the y are given as separate functions of time, i.e., x is a function of t and y is a function of t. Both the x and y are given as in x=x(t), y=y(t). As time changes, the coordinates (x,y) will change producing the graph. Parametric equations are particularly useful in the sciences for representing things that change over time.

You can graph parametric curves manually, but it can be tedious. To graph electronically, check if your grapher can graph parametric equations. If you are using a graphing calculator, go to MODE and look for a graphing option called PARAM or PARAMETRIC. Set it on parametric graphing mode, then go to the area where you enter equations to be graphed. Instead of seeing y1, y2, etc., you should see xt1, yt1, xt2, yt2, etc. Now you are ready to go!

**Objectives**

By the end of this topic you should know and be prepared to be tested on:

- 9.4.1 Manually graph basic parametric equations by creating a chart of t,x,y values and plotting the (x,y) points for each time t
- 9.4.2 Algebraically eliminate the parameter to convert parametric equations to rectangular equations
- 9.4.3 Electronically graph parametric equations recognizing the starting point and direction of spin
- 9.4.4 Electronically graph parametric equations including lines, circles, ellipses, and parabolas
- 9.4.5 Electronically graph parametric equations that have a shift or translation

**Terminology**

Terms you should be able to define: parametric point, parametric equation, parameter