Up

Graphing absolute value equations

The graph of an absolute value equation will be interesting because of the unique nature of absolute value.  Absolute Value is never negative.  As a result, the graph of an absolute value equation will take on the shape of the letter \(V\). 

 

There is an easy procedure you can follow to graph absolute value equations:

  • Plot the value of \(x\) such that the expression inside the absolute value bars is \(0\).
  • Plot one \(x\) value less than that value.
  • Plot one \(x\) value greater than that value.
  • Connect the dots.

 

By strategically choosing the \(x\) value in the first step, we will secure the vertex of the graph, and by plotting one single point less than, and one point greater than that value, we will generate the \(x\) shape easily.  Let’s take a look at an example:

Example:  Graph the equation \(y = \left| x \right| - 4\)

Solution:  We make a table of values.  Following the procedure from above, we first plot that value of \(x\) that would make  \(\left| x \right| = 0\). In this case, the value is \(x = 0\).

\(x\) \(y = \left| x \right| - 4\)
   
0 -4
   

 

Next we want to plot a single value of \(x\) less than \(0\), and a value of \(x\) greater than \(0\).  We choose \( - 1\) and \(1\).


\(x\) \(y = \left| x \right| - 4\)
-1 -3
0 -4
1 -3

Now it’s as easy as plotting the points and connecting the dots, remembering that the shape of the graph of an absolute value equation is always the shape of \(V\).  The graph is below.

Graphing-Absolute-Value-Equations-1

Now let’s try one more example.

Example:  Graph the equation \(y = \left| x \right| + 1\)

Solution:  Again, we plot the value of \(x\) such that \(\left| x \right| = 0\). That is \(x = 0\). Then we plot \(x =  - 1\) and \(x = 1\),  that we have one value less than 0, and one value greater than 0.

\(x\) \(y = \left| x \right| + 1\)
-1 2
0 1
1 2

 

Here is the graph:

Graphing-Absolute-Value-Equations-2

Below you can download some free math worksheets and practice.


Downloads:
5281 x

Graph each equation.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Linear-Equations-and-Inequalities-Graphing-absolute-value-equations-easy


Watch below how to solve this example:

 

Downloads:
3574 x

Graph each equation.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Linear-Equations-and-Inequalities-Graphing-absolute-value-equations-medium

Watch below how to solve this example:

 

Downloads:
3967 x

Graph each equation.

This free worksheet contains 10 assignments each with 24 questions with answers.

Example of one question:

Linear-Equations-and-Inequalities-Graphing-absolute-value-equations-hard

Watch below how to solve this example:

 
 
 

Facebook PageYouTube Channel

Algebra and Pre-Algebra

Beginning Algebra
Adding and subtracting integer numbers
Dividing integer numbers
Multiplying integer numbers
Sets of numbers
Order of operations
The Distributive Property
Verbal expressions
Beginning Trigonometry
Finding angles
Finding missing sides of triangles
Finding sine, cosine, tangent
Equations
Absolute value equations
Distance, rate, time word problems
Mixture word problems
Work word problems
One step equations
Multi step equations
Exponents
Graphing exponential functions
Operations and scientific notation
Properties of exponents
Writing scientific notation
Factoring
By grouping
Common factor only
Special cases
Linear Equations and Inequalities
Plotting points
Slope
Graphing absolute value equations
Percents
Percent of change
Markup, discount, and tax
Polynomials
Adding and subtracting
Dividing
Multiplying
Naming
Quadratic Functions
Completing the square by finding the constant
Graphing
Solving equations by completing the square
Solving equations by factoring
Solving equations by taking square roots
Solving equations with The Quadratic Formula
Understanding the discriminant
Inequalities
Absolute value inequalities
Graphing Single Variable Inequalities
Radical Expressions
Adding and subtracting
Dividing
Equations
Multiplying
Simplifying single radicals
The Distance Formula
The Midpoint Formula
Rational Expressions
Adding and subtracting
Equations
Multiplying and dividing
Simplifying and excluded values
Systems of Equations and Inequalities
Graphing systems of inequalities
Solving by elimination
Solving by graphing
Solving by substitution
Word problems