Review – Parametric Equations

Parametric equations are a method of graphing using an additional parameter, which represents progressive variables such as time. Mostly, this variable is denoted by t. I will provide a quick example to clarify this method of graphing:

x = 2t

y = t²

First, we need to eliminate the variable t. To do this, we need to find a way to make x and y equal to the same value.

x/2 = t
√y = t

Now that t is equal to both x/2 and √y, we can simply set the following:

√y = x/2
y = (1/2)x²


Now, all we have to do is graph this equation:

We could have also graphed this by creating a table by incrementing t and then determining the values of x and y for those values of t.

Since t is not shown on the graph, we must label each point plotted on the line with t = (value of t at that point), so as to indicate the direction in which the graph is progressing. Also, an arrow can be used to indicate this direction.