Question

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

$x=-2y^2$

Short answer

On graphing the equation we get,

Step-by-step solution

Step 1. Given information.

Consider the given equation,

$x=-2y^2$

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

$a=-2$

Then the parabola opens to the left.

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

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

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

Step 2. Find the vertex point.

Substitute $y=0$in the original equation,

$$\begin{gathered} x=-2{\left(0\right)}^2 \\ x=-0 \end{gathered}$$

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
-2	1
-8	2

Plot the points symmetric to localid="1645206574723" $\left(-2,1\right)$and localid="1645206582053" $\left(-8,2\right)$ across the y-axis, the points $\left(-2,-1\right)$and $\left(-8,-2\right)$.

Step 3. Graph the equation.

Plot the graph,