How do you graph $ {(x - 3)^2} + {(y + 1)^2} = 9? $

Hint: If observing the given equation carefully, one could find out that this equation is an equation of circle expressed in center radius form. So to draw its graph simply find coordinates of its center first, and then find out the radius of the circle from the equation. Now you will have the coordinates of the center and the radius, what else do you need to draw a circle? Just draw it.

Complete step by step solution:
In order to graph the given equation $ {(x - 3)^2} + {(y + 1)^2} = 9 $ we can see that this equation is similar to the center radius form of equation of a circle, which is given as
\[{(x - a)^2} + {(y - b)^2} = {r^2},\;{\text{where}}\;(a,\;b)\;{\text{and}}\;r\] are the coordinate of the center of the circle and radius of the circle respectively.
Coming to the given equation of the circle, we can write it as
 $ {(x - 3)^2} + {(y + 1)^2} = 9 \Leftrightarrow {(x - 3)^2} + {(y - ( - 1))^2} = {3^2} $
Now, on comparing the given center radius form of the circle with the general form of center radius form of a circle, we get coordinates of center of the circle and its radius as
 $ (a,\;b) \equiv (3,\; - 1)\;{\text{and}}\;r = 3 $
So we have the coordinates and the radius, so graphing the equation of the circle as follows



Note: When graphing a circle, firstly locate its center on the graph and then take a drawing compass and take the length of radius of the circle in it. Then put the compass pin at the center of the circle and simply draw the required circle by moving the compass a whole round.