Chapter 1, Problem 8CT

To determine

To graph: The equation $y^2=x$ .

Explanation of Solution

Given information:

The equation $y^2=x$ .

Graph:

The graph of $y^2=x$ consistsof 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.

Interpretation:

The graph of the equation $y^2=x$ represents the equation of a parabola.