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:
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∴ 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:
- x = 2t
- 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:
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This gets substituted into (2):
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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.