Answer
See graph, $(-4,2)$ and $(0,0)$
Work Step by Step
Step 1. Graph the given equations
$\begin{cases} (y-2)^2=x+4 \\ y=-\frac{1}{2}x \end{cases}$
as shown in the figure.
Step 2. We can identify the intersection points as $(-4,2)$ and $(0,0)$
Step 3. Check the solutions in the first equation:
$ ((2)-2)^2=(-4)+4=0$
and
$((0)-2)^2=(0)+4=4$
Step 4. Check the solutions in the second equation:
$ (2)=-\frac{1}{2}(-4)$
and
$ (0)=-\frac{1}{2}(0)$
