Answer
We graph the lower part by graphing
$y=2-\sqrt{9-(x+1)^{2}}$
(See below for alternative.)
Work Step by Step
Complete the squares
$(x^{2}+2x)=(x^{2}+2x+1)-1=(x+1)^{2}-1$
$4y-y^{2}=-(y^{2}-4y+2^{2}-2^{2})=-(y-2)^{2}+4$
Rewrite the given equation, and solve for y.
$(x+1)^{2}-1=4-(y-2)^{2}+4$
$(y-2)^{2}=9-(x+1)^{2}$
$y-2=\pm\sqrt{9-(x+1)^{2}}$
$y=2\pm\sqrt{9-(x+1)^{2}}$
and we graph the lower part by graphing
$y=2-\sqrt{9-(x+1)^{2}}$
Note:
with calculators such as desmos, there is an alternate way:
We find from above, that the equation is equivalent to
$(x+1)^{2}+(y-2)^{2}=9$
(circle centered at (-1,2), radius 3.)
Place a restriction on y, allowing y to be 2 or below 2.
See below.
