Question

In the following exercise graph each equation by using its properties:

$x=2y^2$

Short answer

The graph of parabola can be given as

Step-by-step solution

Given information

We are given a equation$x=2y^2$

Find whether the parabola opens right or left

As the coefficient of square term is negative the parabola opens to the Right

Find the axis of symmetry

The axis of symmetry can be given as $y=-\frac{b}{2a}$

Substituting the values we get

$$\begin{gathered} y=-\frac{0}{-2} \\ y=0 \end{gathered}$$

Find the vertex of parabola

To find vertex put $y=0$in the parabola equation

role="math" localid="1645503997034" $$\begin{gathered} x=2{\left(0\right)}^2 \\ x=0 \end{gathered}$$

The vertex is$(0,0)$

Find y-intercept

Put $x=0$

We get,

$$\begin{gathered} 0=2y^2 \\ y=0 \end{gathered}$$

Find x-intercept

Put $y=0$

we get,

$x=0$

plot the graph

The graph can be given as

Conclusion

The graph of parabola can be given as