Graphing Absolute Value Equations
y = | x |

The Absolute Value of a number is the distance a number is from zero on the number line.

Because distance is always a positive number, the negative numbers are considered as a distance measurement which results in a positive answer. Therefore, the Absolute Value function takes all numbers and turns them positive.

For example, the integer negative three is 3 spaces away from zero. The absolute value of negative three is positive three.
Example:
|-3| = 3

The absolute value symbol looks like 2 parallel lines:
| |
Any number inbetween the vertical bars is automatically turned positive.

Example:
| -4 | = 4
| -3 | = 3
| -2 | = 2
| -1 | = 1
| 0 | = 0
| 1 | = 1
| 2 | = 2
| 3 | = 3
| 4 | = 4

This pattern continues for all positive or negative numbers, including decimals and fractions.

Graphing Absolute Value Equations

The graph of an Absolute Value function always maintains a "V"-shaped graph.
You can use a Table of Values to graph any absolute value equation.

Example: Graph y = | x + 2 |

Example: Graph y = | x + 4 |

Rule:
Notice that the v-shaped graph's vertex moves away from the origin when numbers are added or subtracted inside the absolute value sign. This moves the vertex left if addition is involved, and right when subtraction is involved. Sometimes you will need to adjust the numbers in your table in order to make sure that the vertex of the graph is shown.
This is mandatory when you graph an absolute value function.