Absolute Value Part 1
 y = a|x - h| + k

Enter a = 1, h = 0, k = 0   
gives y = 1| x - 0|+ 0  or y = | x |

Click Graph, then Click Store.
Use this graph to compare 

1 . Enter a = 1, h = 0, k = -2 

Predict which way the graph will SHIFT?
Up Left None
Down

Right

Now click Graph.

2. Enter a = 1, h = 0, k = 1 

Predict which way the graph will SHIFT?
Up Left None
Down

Right

Now click Graph.

3. Enter a = 1, h = 0, k = -5/2 

Predict which way the graph will SHIFT?
Up Left None
Down

Right

Now click Graph.
Absolute Value Part 2
 y = a|x - h| + k

Enter a = 1, h = 0, k = 0   
gives y = 1| x - 0| + 0  or y = | x |

Click Graph, then Click Store.
Use this graph to compare 

1 . Enter a = 1, h = 3, k = 0 

Predict which way the graph will SHIFT?
Up Left None
Down

Right

Now click Graph.

2. Enter a = 1, h = -1, k = 0 

Predict which way the graph will SHIFT?
Up Left None
Down

Right

Now click Graph.

3. Enter a = 1, h = 5/3, k = 0 

Predict which way the graph will SHIFT?
Up Left None
Down

Right

Now click Graph.
Absolute Value Quick Quiz
Without graphing predict which way the graph will shift from  y = | x|

 1.  y = |x + 2|

Predict which way the graph will SHIFT?
Up 2 Left 2 None
Down 2

Right 2

Verify with grapher on the left.

 2.  y = | x| + 3

Predict which way the graph will SHIFT?
Up 3 Left 3 None
Down 3

Right 3

Verify with grapher on the left.

 3.  y = |x - 3|  

Predict which way the graph will SHIFT?
Up 3 Left 3 None
Down 3

Right 3

Verify with grapher on the left.

 4.  y = | x| - 1

Predict which way the graph will SHIFT?
Up 1 Left 1 None
Down 1

Right 1

Verify with grapher on the left.
Absolute Value Part 3
 y = a|x - h| + k

Enter a = 1, h = 0, k = 0   
gives y = 1| x - 0| + 0  or y = | x |

Click Graph, then Click Store.
Use this graph to compare 

1 . Enter a = 1/3, h = 0, k = 0 

Predict which way the graph will CHANGE?
Vertical Shrink - widen None
Vertical Stretch - narrow
Now click Graph.

2. Enter a = 3, h = 0, k = 0 

Predict which way the graph will CHANGE?
Vertical Shrink - widen None
Vertical Stretch - narrow
Now click Graph.

3. Enter a = -2, h = 0, k = 0 

Predict which way the graph will CHANGE?
Reflect across  x -axis None
Reflect across  y -axis
Now click Graph.

4. Enter a = 1/10, h = 0, k = 0 

Predict which way the graph will CHANGE?
Vertical Shrink - widen None
Vertical Stretch - narrow
Now click Graph.

5. Enter a = -1, h = 0, k = 0 

Predict which way the graph will CHANGE?
Reflect across  x -axis None
Reflect across  y -axis
Now click Graph.
Absolute Value Altogether
Predict the following shifting, then verify using grapher.
y = 2| x - 3 |  + 4
y = -2| x + 3 |  - 4
y = 1/4| x + 2 |  + 1
y = -4| x - 1 |  -  2
y = | x - 2/5 | - 1/5
 
Absolute Value Part 4
 y = a|x - h| + k
Although most books won't call the point (h,k) the vertex (as in quadratics) but it will either be a maximum or minimum value for the absolute value function.
If a > 0 , then (h,k) is the lowest point of the graph.  (opens upward)
If a < 0 , then (h,k) is the highest point of the graph.  (opens downward)

Examples: 

Absolute Value Min or Max
y = |x - 1/2 | + 3/5 (1/2, 3/5) Min
y = -2 |x + 3 | - 4 (-3,-4) Max
y = 3|x + 1|   (-1,0) Min
y = -2|x|  - 4 (0,-4) Max
y = 2 |x - 3|  + 4 (3,4) Min