Parametric Equations

Sometimes the input variable, x, and the output variable, y, of an equation might be influenced by a separate factor, t. In other words, the variable, t, influences both the x and the y separately. Such a scenario can be modeled using a parametric. For example, finding the solution to x = t + 1 and y = t ÷ 2 at t = 4 gives the ordered pair:


∴   Ordered pair: (8, 2)

Notice how the ordered pairs generated from the parametric equations form a parabola. If you’d like to find out the equation to the curve without creating a table of values, you can isolate t from one equation and substitute it into the other equation. The equations again were:

  1.   x = 2t
  2.   y = t² – 2

The easier of the two equations to isolate for t is (1) because all you need to do is divide both sides of 2:


This gets substituted into (2):


The equation in terms of x-y is called a Cartesian equation, and will produce the exact same parabola as the one in the video.