1. 2.5 Absolute Value Functions and Graphs
Graphing NEGATIVE
Absolute Value Functions

2. Negative Absolute Value Functions
The vertex is a MAXIMUM
Negative absolute value functions open DOWN

3. Finding the Vertex For an equation y = -|mx + b| + c, vertex = -b , c
Example: Find the vertex of y = -|x + 1| - 2

4. Finding the Vertex For an equation y = |mx + b| + c, vertex = -b , c m
Example: Find the vertex of y = -|x + 1| - 2
Answer: = -1 , -2 1
= -1 , -2

5. Absolute Value Functions
Steps to graphing a negative absolute value function…
Find the vertex
Write two linear equations and find slope
Use slope to plot points, connect the dots

6. Absolute Value Functions
Example 1:
Graph y = -|3x + 12|

7. Absolute Value Functions
Step 1: Find the vertex
y = -|3x |
m = -b = c =

8. Absolute Value Functions
Step 1: Find the vertex
y = -|3x |
m = b = c = 0

9. Absolute Value Functions
Step 1: Find the vertex
y = -|3x |
m = b = c = 0
vertex = -b , c m
vertex = -12 , 0 3
vertex = (-4, 0)

10. Absolute Value Functions
Step 1: Find the vertex
vertex = (-4, 0)

11. Absolute Value Functions
Step 2: Write two linear equations and find slope.
y = -|3x + 12|
Positive Negative

12. Absolute Value Functions
Step 2: Write two linear equations and find slope.
y = -|3x + 12|
Positive Negative
y = -3x y = -(-3x – 12)
y = 3x + 12
m1 = m2 = 3

13. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = -3
m2 = 3

14. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = -3
m2 = 3

15. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = -3
m2 = 3

16. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = -3
m2 = 3

17. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = -3
m2 = 3

18. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = -3
m2 = 3

19. Absolute Value Functions
Example 2:
Graph y = -|3x + 6| - 2

20. Absolute Value Functions
Step 1: Find the vertex
y = -|3x + 6| - 2

21. Absolute Value Functions
Step 1: Find the vertex
y = -|3x + 6| - 2
m = 3 -b = -6 c = -2
vertex = (-6/3, -2)
= (-2, -2)

22. Absolute Value Functions
Step 1: Find the vertex
vertex = (-2, -2)

23. Absolute Value Functions
Step 2: Write two linear equations and find slope
y = -|3x + 6| - 2
Positive Negative

24. Absolute Value Functions
Step 2: Write two linear equations and find slope
y = -|3x + 6| - 2
Positive Negative
y + 2 = -(3x + 6) y + 2 = -[-(3x + 6)]
y + 2 = -3x – 6 y + 2 = 3x + 6
y = -3x – y = 3x + 4

25. Absolute Value Functions
Step 2: Write two linear equations and find slope
y = -|3x + 6| - 2
Positive Negative
y + 2 = -(3x + 6) y + 2 = -[-(3x + 6)]
y + 2 = -3x – 6 y + 2 = 3x + 6
y = -3x – y = 3x + 4
m1 = m2 = 3

26. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3

27. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3

28. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3

29. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3

30. Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3

31. Homework
p.90 #7-9, 22, 40, 44, 45