## Precalculus (6th Edition) Blitzer

We know that the parametric equations are the equations having a common variable in both x and y. And by taking the values of t manually, one can get the values of x and y separately. And the corresponding points can be plotted to get a graph of the given parametric equations. For example: If the parametric equations are as given below: \begin{align} & x=t \\ & y=2{{t}^{2}} \\ \end{align} Take the values of t manually and compute the values of x and y as given below: For $t=1$ \begin{align} & x=t \\ & =1 \end{align} \begin{align} & y=2{{t}^{2}} \\ & =2{{\left( 1 \right)}^{2}} \\ & =2 \end{align} Similarly, for $t=2$ \begin{align} & x=t \\ & =2 \end{align} \begin{align} & y=2{{t}^{2}} \\ & =2{{\left( 2 \right)}^{2}} \\ & =8 \end{align} And take some more values of t and get the values of x and y as given below: \begin{align} & t=3 \\ & x=3 \\ & y=18 \\ \end{align} \begin{align} & t=4 \\ & x=4 \\ & y=32 \\ \end{align} Thus, take these values of x and y to plot the graph as drawn below: 