Question

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

Answer 1

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

Explanation:

`x^2 + (y+2)^2 = 9`

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

Let's modify it to read

`(x-0)^2 + (y+2)^2 = 9`

Now we see that it is a circle with centre at (`0,-2`) and radius `sqrt9 = 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.

And you have your graph.