Question

In the following exercises, graph each equation by using properties.

$x=3y^2$

Short answer

On graphing the equation we get,

Step-by-step solution

Step 1. Given information.

Consider the given equation,

$x=3y^2$

Compare $x=a{y}^2+by+c$with the given equation,

$a=3$

Then the parabola opens to the right.

To find the axis of symmetry, find $y=-\frac{b}{2a}$. Then,

$$\begin{gathered} y=-\frac{0}{2\left(3\right)} \\ y=0 \end{gathered}$$

The vertex is on the line $y=0$.

Step 2. Find the vertex point.

Substitute $y=0$in the original equation,

localid="1645207023473" $$\begin{gathered} x=3{\left(0\right)}^2 \\ x=0 \end{gathered}$$

Therefore, the vertex is $\left(0,0\right)$.

Since the vertex is $\left(0,0\right)$, both the x- and y-intercepts are the point $\left(0,0\right)$.

Substitute various values of y,

x	y
3	1
12	2

Plot the points symmetric to localid="1645207394384" $\left(3,1\right),\left(12,2\right)$across the y-axis, the points $\left(3,-1\right),\left(12,-2\right)$.

Step 3. Graph the equation.

Plot the graph,