Author:
Craig Coletta

This lesson will demonstrate how to graph the solution set of an absolute value equation.

Tutorial

This is an example of the graph of an** absolute value equation** y=|x+2|.

Remember that the **absolute value** of a number can best be expressed as “*the number of steps away from zero, in either a positive or negative direction, you must take in order to reach a number.*”

Thus, the absolute value of 2 is 2 – two steps away from zero.

The absolute value of -2 is ALSO 2 – two steps away from zero. An absolute value can therefore **NEVER** be a negative number.

The absolute value of negative 2 is written as |-2|, The bars on either side of the number illustrate that the absolute value of the number is being represented.

So imagine an equation like this:

**y=|x+2|**

In this example, no matter what value is plugged in for x, y can never be a negative number: if x is -3, the equation simplifies to:

**y=|-3+2|**

giving the result:

**y=|-1|**

Since the absolute value of -1 = 1, y=1

In this example, the lowest possible value of y is 0, and as the value of x moves further into negative numbers, the value of y will become larger and larger positive numbers. Thus the graph appears as an upward-pointing “V” shape with its vertex at 0 and positive or negative values of x producing larger and larger positive values for y..

An equation such as x=|y+2| would yield a rightward-pointing “V” shape (Try graphing this as an example.