# How do you graph x^2 + (y + 2)^2 = 9?

Jul 8, 2015

You convert the equation to standard form, determine the centre, vertices, and endpoints. Then you plot the graph.

#### Explanation:

${x}^{2} + {\left(y + 2\right)}^{2} = 9$

This is almost the standard form for the equation of a circle.

${\left(x - 0\right)}^{2} + {\left(y + 2\right)}^{2} = 9$

Now we see that it is a circle with centre at ($0 , - 2$) and radius $\sqrt{9} = 3$.

This means that, to find the vertices, you go 3 units up from the centre and 3 units down.

Thus, the vertices are at ($0 , 1$) and ($0 , - 5$).

To find the endpoints, you go 3 units left of the centre and 3 to the right.

Thus, the endpoints are at ($- 3 , - 2$) and ($3 , - 2$).

Plot these points on a graph.

Now draw a smooth circle through these four points.