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