Example 4: Part of a parabola

The parametric curve or trajectory for these parametric equations is part of the graph of the function $y=x^2$ .

$$\left. \begin{array}{lclcl} x &=& f(t) &=& t\\ y &=& g(t) &=& t^2\\ \end{array}\right\}\quad 0\leq t\leq 3$$

This is another example where $x=f(t)$ is the identity function $x=t$ .

The parametric curve will be the same as the graph of $y=g(x)=x^2$ .