# Question #9cf14

Feb 6, 2018

Graph the function using a table of values, making sure to include the vertex.

#### Explanation:

The general form of an absolute value equation is $f \left(x\right) = a | x - h | + k$.

Where:
$a$ is the vertical stretch (if $| a |$ is > 1) or shrink (if $| a |$ is < 1)
If $a$ is negative, the graph is reflected horizontally.

$h$ is the horizontal shift

$k$ is the vertical shift

To graph using transformations, we look at the parent function (in this case $f \left(x\right) = | x |$ and apply the transformations to the x and y values of the table of values. The x-values of the parent function will be modified by adding or subtracting the $h$ value of the transformed function. The y-values of the parent function will first be multiplied be the $a$ value of the transformed function, and then modified by adding or subtracting the $k$ value.

In the example provided above, $H \left(x\right) = - | x + 2 |$ so:

$a$ = -1
$h$ = -2 (-$h$=+2, so $h$=-2)
$k$ = 0

The table of values for the parent function looks like this:

X | Y

-2 | 2
-1 | 1
0 | 0
1 | 1
2 | 2

The transformed table of values would look like this:

X + h | aY + k

-2-2=-4 | -1(2)+0=-2
-1-2=-3 | -1(1)+0=-1
0-2=-2 | -1(0)+0=0
1-2=-1 | -1(1)+0=-1
2-2=0 | -1(2)+0=-2