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2.5 Absolute Value Functions and Graphs
Graphing NEGATIVE Absolute Value Functions
Negative Absolute Value Functions
The vertex is a MAXIMUM
Negative absolute value functions open DOWN
Finding the Vertex
For an equation y = -|mx + b| + c,
vertex = -b , c
m
Example: Find the vertex of y = -|x + 1| - 2
Finding the VertexFor an equation y = |mx + b| + c,
vertex = -b , c m
Example: Find the vertex of y = -|x + 1| - 2Answer: = -1 , -2
1= -1 , -2
Absolute Value Functions
Steps to graphing a negative absolute value function…
1. Find the vertex
2. Write two linear equations and find slope
3. Use slope to plot points, connect the dots
Absolute Value Functions
Example 1:
Graph y = -|3x + 12|
Absolute Value Functions
Step 1: Find the vertex
y = -|3x + 12|
m = -b = c =
Absolute Value Functions
Step 1: Find the vertex
y = -|3x + 12|
m = 3 -b = -12 c = 0
Absolute Value FunctionsStep 1: Find the vertex
y = -|3x + 12|
m = 3 -b = -12 c = 0
vertex = -b , cm
vertex = -12 , 0 3
vertex = (-4, 0)
Absolute Value FunctionsStep 1: Find the vertex
vertex = (-4, 0)
Absolute Value Functions
Step 2: Write two linear equations and find slope.
y = -|3x + 12|
Positive Negative
Absolute Value Functions
Step 2: Write two linear equations and find slope.
y = -|3x + 12|
Positive Negative y = -3x - 12 y = -(-3x – 12)
y = 3x + 12
m1 = -3 m2 = 3
Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = -3
m2 = 3
Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = -3
m2 = 3
Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = -3
m2 = 3
Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = -3
m2 = 3
Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = -3
m2 = 3
Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-4, 0)
m1 = -3
m2 = 3
Absolute Value Functions
Example 2:
Graph y = -|3x + 6| - 2
Absolute Value FunctionsStep 1: Find the vertex
y = -|3x + 6| - 2
Absolute Value FunctionsStep 1: Find the vertex
y = -|3x + 6| - 2
m = 3 -b = -6 c = -2
vertex = (-6/3, -2)
= (-2, -2)
Absolute Value Functions
Step 1: Find the vertex
vertex = (-2, -2)
Absolute Value FunctionsStep 2: Write two linear equations
and find slope
y = -|3x + 6| - 2
Positive Negative
Absolute Value FunctionsStep 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 – 8 y = 3x + 4
Absolute Value FunctionsStep 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 – 8 y = 3x + 4
m1 = -3 m2 = 3
Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3
Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3
Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3
Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3
Absolute Value Functions
Step 3: Use the slope to plot points
vertex = (-2, -2)
m1 = -3
m2 = 3
Homework
p.90 #7-9, 22, 40, 44, 45
