In Pre-Calc 11 this week we looked at graphing Absolute Functions, and in this blog post, I’ll be giving an example of how absolute value functions graphs differently than regular quadratic or linear functions.

Usually, without the Absolute value signs, this graph would look like this with an X

intercept of 1.5,0 and a slope of 2 over 1.

But with absolute values, a number can never have a negative value, meaning the lower portion of the line cannot go below zero.

Since the X intercept is at x=1.5 (in this case this point is known as the “Critical Point”) that is where the line will bounce back up. Looking like this

Graphing absolute quadratic functions works similarly but is a little bit more complicated.

If we take this quadratic function and graph it, it will look like this,  

 

 

 

It opens up, has a vertex of 0,-4, and is congruent to But since absolute values cannot have any negative value, all of the coordinates below the critical points, or x-intercepts,  -2,0 and 2,0 have to be inverted. Resulting in a parabola (I don’t know if it still qualifies as a parabola actually) with a vertex that is mirrored from it’s original, negative, coordinate. That looks like this.