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.

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:

Below you can **download** some** free** math worksheets and practice.

Graph each equation.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**

Graph each equation.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**

Graph each equation.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**