Parametric Equations

Tables & Graphs

Back when you first began learning how to graph functions, you probably started by building \(x | y\) tables, selecting various \(x\)-values that you plugged into the \(y = f(x)\) function to compute the corresponding \(y\)-values. Then you could use the \((x,y)\) paired values to plot points on the graph. We can basically do the same thing with parametric equations, but now we will be constructing \(t | x | y\) tables. We get to choose the \(t\)-values that we want to use to compute both the \(x\) and \(y\) values, and then we can plot the \((x,y)\) coordinates. We will also want to denote the direction or positive orientation of the curves as we draw them. Let's look at a few examples.