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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 $=$.

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Jason Chen
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  • See @Jared's answer to your previous question. Basically, find the part of the graph in the first quadrant by taking $x,y\ge0$ so that you get the familiar equation $(x-1)^2+(y-1)^2=2$. Then copy this bit symmetrically in every other quadrant. – David May 13 '14 at 04:26
  • Why is it copied symmetrically, though? What part of the equation does that? – Jason Chen May 13 '14 at 04:28
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    In Quadrant I, $|x| = x$, $|y| = y$. In Quadrant II, $|x| = -x$, $|y|=y$. Etc... – Braindead May 13 '14 at 04:29
  • post it in an answer – Jason Chen May 13 '14 at 04:30

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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.

Braindead
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