Today in class we briefly reviewed the fundamentals of parametric equations. Parametric equations are three-dimensional graphs that relate a point in a plane to a corresponding value of time, t. Every function has an infinite number of parametric equations that can be associated with it. Using the example illustrated in my notes, it can be seen that the graph y=x^2 can be represented parametrically with both x=t, y=t^2, and x=sint, y=(sint)^2. The only difference between the two graphs is that x=sint, y=(sint)^2 is bounded by [-1,1] and oscillates because of the behavior of the sin function.
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