This week in my intermediate algebra class we covered graphing absolute value functions. I began by having students create an x-y table for . We plotted the points and they could tell the shape of the graph, and I asked them which point was the most important point. They knew it was the turning point of the graph. So far, so good.

Next, I put up this equation: . I then gave them a few minutes to figure out where the turning point would be, in other words, which value of x would produce the smallest value of y. After some trial and error the groups found the turning point to be (4, 2). I graphed the equation using Desmos and confirmed their answer. I followed up with another function, , and asked them if they could quickly determine the coordinates of the turning point. I had a student explain how she found it, and the class liked her explanation. I went into depth about why the turning point was located at (1, -3) in terms of minimizing the output of the absolute value, then shifted into a discussion of (h, k) (see what I did there?).

Students benefit from having the opportunity to think and discover, rather than being told what to do.

On Wednesday we will move on to tying the graph of an absolute value function to the solutions of absolute value equations and inequalities. I gave the class a quick preview at the end of class, and I could see that some of the students who were struggling with the symbolic math began to understand what the solutions represented. I will blog about our experience and let you know how it went.