<p>A parametric function is a function that is split up into two components. It has a constant incrementor "t" which starts at 0 and goes up from there.

For example:

x = t

y = 2t</p>

<p>The point at t= 0 would be (0,0) at t=1 it would (t,2t) or (1,2) since t= 1, at t=2 it would be (t,2t) or (2,4).

I like to think of T as time, you can't have negative time and it increases naturally to infinity and as t changes so do the coordinates it represents.</p>

<p>Eliminating the Parameter: (Find an XY function that represents the parametric function)

Method 1: Substitution.

Example:

y=t^3

x=t^2

What I like to do is solve for X in terms of t and then "substitute" x into the y equation.

sqrt(x)=t

therefore,

y=(sqrt(x))^3

= x^(3/2)

y = x^3/2

Method 2: Using Trig Identities

x= (sin t)^2

y=(cos t)^2

Now remember cos^2(any number)+sin^2(any number)= 1 where the (any number) is the same in both of cos^2 and sin^2 is always equal to 1.

So just substitute, t is the same in both, therefore x+y = 1

or y=-x+1</p>