Absolute
Value Part 1 
y
= ax
 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? 

Now click Graph. 
2. Enter a
= 1,
h = 0, k =
1

Predict
which way the graph will SHIFT? 

Now click Graph. 
3. Enter a
= 1,
h = 0, k =
5/2

Predict
which way the graph will SHIFT? 

Now click Graph. 
Absolute
Value Part 2 
y
= ax
 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? 

Now click Graph. 
2. Enter a
= 1,
h = 1, k =
0

Predict
which way the graph will SHIFT? 

Now click Graph. 
3. Enter a
= 1,
h = 5/3, k =
0

Predict
which way the graph will SHIFT? 

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? 

Verify
with grapher on the left. 
2. y
=  x + 3 
Predict
which way the graph will SHIFT? 

Verify
with grapher on the left. 
3. y
= x  3

Predict
which way the graph will SHIFT? 

Verify
with grapher on the left. 
4. y
=  x  1 
Predict
which way the graph will SHIFT? 

Verify
with grapher on the left. 
Absolute
Value Part 3 
y
= ax
 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? 

Now click Graph. 
2. Enter a
= 3,
h = 0, k =
0

Predict
which way the graph will CHANGE? 

Now click Graph. 
3. Enter a
= 2,
h = 0, k =
0

Predict
which way the graph will CHANGE? 

Now click Graph. 
4. Enter a
= 1/10,
h = 0, k =
0

Predict
which way the graph will CHANGE? 

Now click Graph. 
5. Enter a
= 1,
h = 0, k =
0

Predict
which way the graph will CHANGE? 

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
= ax
 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
= 3x + 1

(1,0)
Min 
y
= 2x
 4 
(0,4)
Max 
y
= 2 x  3
+ 4 
(3,4)
Min 