# Absolute value graphs review

CCSS Math: HSF.IF.C.7, HSF.IF.C.7b

The general form of an absolute value function is f(x)=a|x-h|+k. From this form, we can draw graphs. This article reviews how to draw the graphs of absolute value functions.

General form of an absolute value equation:

The variable $\goldD{a}$ tells us how far the graph stretches vertically, and whether the graph opens up or down. The variables $\blueD h$ and $\blueD k$ tell us how far the graph shifts horizontally and vertically.

Some examples:

### Example problem 1

We're asked to graph:

First, let's compare with the general form:

The value of $\goldD a$ is $1$, so the graph opens upwards with a slope of $1$ (to the right of the vertex).

The value of $\blueD h$ is $1$ and the value of $\blueD k$ is $5$, so the vertex of the graph is shifted $1$ to the right and $5$ up from the origin.

Finally here's the graph of $y=f(x)$:

### Example problem 2

We're asked to graph:

First, let's compare with the general form:

The value of $\goldD a$ is $-2$, so the graph opens downwards with a slope of $-2$ (to the right of the vertex).

The value of $\blueD h$ is $0$ and the value of $\blueD k$ is $4$, so the vertex of the graph is shifted $4$ up from the origin.

Finally here's the graph of $y=f(x)$:

*Want to learn more about absolute value graphs? Check out this video.*

*Want more practice? Check out this exercise.*