Dissection of strange graph

Question

I want to know why the graph in Strange graph problem looks how it does. Can someone explain? Here's the inequality:

$(|x|−1)^2+(|y|−1)^2<2$

You can graph this equation at https://www.desmos.com/calculator. Make sure to change the $<$ to $=$.

Answer 1

Very often, people get intimidated by the absolute value sign (myself included), but it's really simple if you break it apart.

In Quadrant I: $x,y\ge0$, so $|x| = x$ and $|y| = y$. In Quadrant II: $x\le0$, $y\ge0$, so $|x| = -x$ and $|y| = y$, etc.

By removing the absolute values in this way, one obtains equations of circles in the appropriate quadrants.