+
Absolute Value Graph

# Absolute Value Graph

Author: Craig Coletta
##### Description:

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

(more)

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to many different colleges and universities.*

No credit card required

46 Sophia partners guarantee credit transfer.

299 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 33 of Sophia’s online courses. Many different colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.

Tutorial ## Absolute Value Graph

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.

Rating