how to draw this graph plz explain in detail

Question

y  =    |  x^2-  2  |     how to draw graph of such equation

Comments

firstly put inside mod part =0(it will give points where mod changes its behaivior)

 x² - 2 = 0

x= $\sqrt{2}$ , $-\sqrt{2}$

using inequality principle you will find that,

y >=0 , x belongs (-$\infty$ , $-\sqrt{2}$ ] $\cup$ [$\sqrt{2}$ , $\infty$)

  < 0  , x belongs ($\sqrt{2}$ , $-\sqrt{2}$)

divide regions like this,

y = {  x² - 2, x belongs (-$\infty$ , $-\sqrt{2}$ ] $\cup$ [$\sqrt{2}$ , $\infty$) // upward parabola

   =   2 - x² , x belongs ($-\sqrt{2}$, $\sqrt{2}$) // downward parabola

}

corresponding graph,

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here what the dotted line represents ??

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you have taken mirror image of dotted part

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thnks bro got it :)

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in last line though it dont have effect   2 - x² , x belongs  to ( --- √2 ,   √2)   //  downward parabola correct me if iam wrong

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yes you are correct,

edited.