# Absolute value graphs review

CCSS Math: 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:
$f(x)=\goldD{a}|x-\blueD{h}|+\blueD{k}$
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:
Graph of y=|x|
Graph of y=3|x|
Graph of y=-|x|
Graph of y=|x+3|-2

### Example problem 1

$f(x)=|x-1|+5$
First, let's compare with the general form:
$f(x)=\goldD{a}|x-\blueD{h}|+\blueD{k}$
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

$f(x)=-2|x|+4$
$f(x)=\goldD{a}|x-\blueD{h}|+\blueD{k}$
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 $y=f(x)$: