Graph an absolute value function

You can quickly graph an absolute value function using the vertex and a table of values.

Note that the vertex is the sharp corner of the graph!

Example #1

Graph f(x) = |2x + 6|

The general form of the function is f(x) = |mx + b| + c

Using f(x) = |2x + 6|, m = 2, b = 6, and c  = 0

First, find the vertex.

As seen in the lesson about absolute value function, the vertex is located at (-b / m, c)

Therefore, the vertex is (-6 / 2, 0) or (-3, 0)

Now, evaluate the function for several selected values of x.

x -5 -4 -2 -1 0
f(x) 4 2 2 4 6

The graph of the absolute value function is shown below

Graph of absolute value function

Example #2

Graph f(x) = |-3x + 15| + 1

The general form of the function is f(x) = |mx + b| + c

Using f(x) = |-3x + 15| + 1, m = -3, b = 15, and c  = 1

First, find the vertex.

The vertex is located at (-b / m, c) or (-15 / -3, 1) or (5, 1)

The vertex is (-6 / 2, 0) or (-3, 0)

Now, evaluate the function for several selected values of x.

x 3 4 6 7
f(x) 7 4 4 7

The graph of the absolute value function is shown below

Graph of absolute value function

Recent Articles

  1. Box and Whiskers Plot

    Nov 18, 22 08:20 AM

    Easily learn to construct a box and whiskers plot for a set of data by using the median and the extreme values.

    Read More

  2. Binary Number System

    Nov 17, 22 10:53 AM

    This lesson will give you a deep and solid introduction to the binary number system.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes