sketch the parametric curve by plotting points.

$x=t,y=t^2,t\in R$

$x=t,y=t^2,t\in R$

A collection of quantities is defined as a function of one or more independent variables called parameters in a parametric equation.

Consider the parametric curve $x=t,y=t^2$at $t\in \mathrm{ℝ}$

The goal is to draw the parametric curve.

To draw the graph for the parametric equations assume $t=-2,-1,0,1,2$

Substitute different $t$values in the parametric equations and find the values of $x,y$

The point $(x,y)$When $t=2$is,

$(x,y)=\left(t,t^2\right)$

$(x,y)=\left(-2,(-2{)}^2\right)[$since by substituting $t=-2]$

$(x,y)=(-2,4)$simplify

The point $(x,y)$When $t=-1$is,

$$\begin{gathered} (x,y)=\left(t,t^2\right) \\ (x,y)=\left(-1,(-1{)}^2\right)[\text{since by substituting}t=-1] \\ (x,y)=(-1,1)\text{simplify} \end{gathered}$$

The point $(x,y)$When $t=0$is,

$$\begin{gathered} (x,y)=\left(t,t^2\right) \\ (x,y)=\left(0,(0{)}^2\right)\text{[since by substituting}t=0\left] \\ \right(x,y)=(0,0)\text{simplify} \end{gathered}$$

The point $(x,y)$When $t=1$is,

$$\begin{gathered} (x,y)=\left(t,t^2\right) \\ \left.(x,y)=\left(1,(1{)}^2\right)\text{[since by substituting}t=1\right] \\ (x,y)=(1,1)\text{simplify} \end{gathered}$$

The point $(x,y)$ When $t=2$ is,

The tabular representation of the points is as follows,

The graphical representation is shown below,

Therefore, the solution is a required graph.