Parabolas

Here is a simple parabola, or quadratic function.
Its equation is   y = x2 - 3

There is a portion of this graph that is negative. It looks like everything on the graph from x values of about -1.7 to +1.7

When we apply the absolute value bars to this function, the curved part of the parabola that is below the X axis will reflect upwards. Have a look below.




On the right is the graph of the function   y = |x2 - 3|

All of the negative values of this function have become positive.

The portion that was below the X axis has been reflected above the axis.





... now let's look at a cubic function



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