Answer
The graph is shown below
Work Step by Step
The graph of ${{y}^{2}}=x$ consists of points $\left( x,y \right)$.
To graph the equation ${{y}^{2}}=x$, plot some points $\left( x,\,y \right)$ and join them. To find some points $\left( x,\,y \right)$, choose random $y$ values and find the corresponding $x$ values by using the equation${{y}^{2}}=x$.
${{y}^{2}}=x$ can be written as $x={{y}^{2}}$.
So, use $x={{y}^{2}}$ to find the $\left( x,y \right)$ values.
If $y=0$, then $x={{\left( 0 \right)}^{2}}=0$. Therefore, the point $\left( 0,0 \right) $ is on the graph.
If $y=1$, then $x={{\left( 1 \right)}^{2}}=1$. Therefore, the point $\left( 1,1 \right)$ is on the graph.
If $y=-1$, then $x={{\left( -1 \right)}^{2}}=1$. Therefore, the point $\left( 1,-1 \right)$ is on the graph.
If $y=2$, then $x={{\left( 2 \right)}^{2}}=4$. Therefore, the point $\left( 4,2 \right)$ is on the graph.
If $y=-2$, then $x={{\left( -2 \right)}^{2}}=4$. Therefore, the point $\left( 4,-2 \right)$ is on the graph.
If $y=3$, then $x={{\left( 3 \right)}^{2}}=9$. Therefore, the point $\left( 9,3 \right)$ is on the graph.
If $y=-3$, then $x={{\left( -3 \right)}^{2}}=9$. Therefore, the point $\left( 9,-3 \right)$ is on the graph.
If $y=-5$, then $x={{\left( -5 \right)}^{2}}=25$. Therefore, the point $\left( 25,5 \right)$ is on the graph.
If $y=5$, then $x={{\left( -5 \right)}^{2}}=25$. Therefore, the point $\left( 25,-5 \right)$ is on the graph.
Draw the graph by plotting these points and connecting them.
The graph of the equation ${{y}^{2}}=x$ represents the equation of a parabola.
