###### Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

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# Absolute Value Inequality Graphs in Two Variables - Concept

Alissa Fong
###### Alissa Fong

MA, Stanford University
Teaching in the San Francisco Bay Area

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts

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Graphing inequalities with two variables can be tricky and is made even more tricky when we graph inequalities with two variables and absolute value. With absolute value graphing, if the inequality is similar to the equation of a line, (for example y > m|x| + b), then we get a V shape, and we shade above or below the V. This is very similar to graphing inequalities with two variables. The difference is that we are graphing inequalities with absolute values which makes the V-shape.

What we're going to be working on here is how to graph Absolute Value inequalities, Absolute Value inequalities. What I want to do is show you guys a shortcut using a parent function so that when you guys see this in your homework hopefully it will go a little faster. What I mean by parent function is that all graphs of this type look the same, let me show you what they look like.
In order to show you that I've made an xy chart I just chose these x values and I'm going to substitute in them, substitute them in to find the the y values. Like if I put -2 in there, Absolute Value y's it I get +2. By the way Absolute Value y's is not a real word I kind of made that up just between you and me but you can use it if you want to. -1 Absolute Value y becomes +1 go through and fill it out like that point by point, then when you go to graph it you'll see you get this really interesting shape you get a v. What I did was plot the points -2 2, -1 1 like that and then if you connect them shoop you'll see you get a v shape be careful it's not a u it's not a parabola some of you guys already know about that. This is a strict v and that's really interesting all Absolute Value graphs are going to have that shape.