SOLUTION: graph : |x^2-1| I need it in steps, please :) Thank you !

Algebra ->  Absolute-value -> SOLUTION: graph : |x^2-1| I need it in steps, please :) Thank you !       Log On


   

Question 1146889: graph : |x^2-1|
I need it in steps, please :)
Thank you !
Answer by ikleyn(52792) About Me  (Show Source):
You can put this solution on YOUR website!
.
Step 1:  graph  x%5E2+-+1,  without the modulus sign.


         It is simple parabola,  see below


    graph%28+330%2C+330%2C+-5%2C+5%2C+-5%2C+10%2C%0D%0A+++++++++++++++x%5E2-1%0D%0A%29

    Plot  y = x%5E2+-+1.



Step 2.  


    Do you see this part of the parabola between  x= -1  and  x= 1, which is BELOW x-axis ?

    Reflect it about the x-axis, as if this part of the x-axis  -1 <= x <= 1  is a mirror.


    You will get the plot of your ORIGINAL function  y = abs%28x%5E2-1%29.


    graph%28+330%2C+330%2C+-5%2C+5%2C+-5%2C+10%2C%0D%0A+++++++++++++++abs%28x%5E2-1%29%0D%0A%29

    Plot  y = abs%28x%5E2+-+1%29.



Step 3.  Do not forget to post your "THANKS" to me for my lesson.