Question

Sketch the graph of the equation$\mathbf{2}\mathbf{x}\mathbf{+}{\mathbf{y}}^2\mathbf{=}\mathbf{0}$ by making table and plotting points.

Short answer

The graph of equation is a parabola.

Step-by-step solution

Step 1. Re-arrange the equation. 

The given equation can be re-arranged as shown below,

$\begin{array}{c}8x+y^2=\mathrm{0....}\left(\text{Given}\right)\\ \text{or,}{y}^2=-8x\mathrm{....}\left(\text{Rearranged}\right)\end{array}$

Step 2. Construct the table for the re-arranged equation.

The re-arranged equation is$y^2=-8x$ whose tables for respective values of$\left(x\right)$ and$\left(y\right)$ is shown below.

x	0	$-2$	$-2$
y	0	4	$-4$

Step 3. Plot the points on coordinate plane.

By plotting points on coordinate plane, the graph for the equation is shown below.

Step 4. DESCRIPTION OF STEPS.

From the graph it can be interpreted that the graph of the equation represents a parabola.