Answer
See graph, $\left(1,0\right),\left(1,-4\right),(0,\sqrt{3}-2),(0,-\sqrt{3}-2)$
Work Step by Step
1. See graph for equations $(x-1)^2+(y+2)^2=4$ and $y^2+4y-x+1=0$.
2. Per exercise instructions, we can identify the point(s) of intersection as: $\left(1,0\right),\left(1,-4\right),(0,\sqrt{3}-2),(0,-\sqrt{3}-2)$