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**2.5 Absolute Value Functions and Graphs**

Graphing NEGATIVE Absolute Value Functions

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**Negative Absolute Value Functions**

The vertex is a MAXIMUM Negative absolute value functions open DOWN

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**Finding the Vertex For an equation y = -|mx + b| + c, vertex = -b , c**

Example: Find the vertex of y = -|x + 1| - 2

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**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

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**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

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**Absolute Value Functions**

Example 1: Graph y = -|3x + 12|

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**Absolute Value Functions**

Step 1: Find the vertex y = -|3x | m = -b = c =

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**Absolute Value Functions**

Step 1: Find the vertex y = -|3x | m = b = c = 0

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**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)

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**Absolute Value Functions**

Step 1: Find the vertex vertex = (-4, 0)

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**Absolute Value Functions**

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

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**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

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**Absolute Value Functions**

Step 3: Use the slope to plot points vertex = (-4, 0) m1 = -3 m2 = 3

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**Absolute Value Functions**

Step 3: Use the slope to plot points vertex = (-4, 0) m1 = -3 m2 = 3

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**Absolute Value Functions**

Step 3: Use the slope to plot points vertex = (-4, 0) m1 = -3 m2 = 3

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**Absolute Value Functions**

Step 3: Use the slope to plot points vertex = (-4, 0) m1 = -3 m2 = 3

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**Absolute Value Functions**

Step 3: Use the slope to plot points vertex = (-4, 0) m1 = -3 m2 = 3

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**Absolute Value Functions**

Step 3: Use the slope to plot points vertex = (-4, 0) m1 = -3 m2 = 3

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**Absolute Value Functions**

Example 2: Graph y = -|3x + 6| - 2

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**Absolute Value Functions**

Step 1: Find the vertex y = -|3x + 6| - 2

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**Absolute Value Functions**

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

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**Absolute Value Functions**

Step 1: Find the vertex vertex = (-2, -2)

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**Absolute Value Functions**

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

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**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

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**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

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**Absolute Value Functions**

Step 3: Use the slope to plot points vertex = (-2, -2) m1 = -3 m2 = 3

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**Absolute Value Functions**

Step 3: Use the slope to plot points vertex = (-2, -2) m1 = -3 m2 = 3

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**Absolute Value Functions**

Step 3: Use the slope to plot points vertex = (-2, -2) m1 = -3 m2 = 3

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**Absolute Value Functions**

Step 3: Use the slope to plot points vertex = (-2, -2) m1 = -3 m2 = 3

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**Absolute Value Functions**

Step 3: Use the slope to plot points vertex = (-2, -2) m1 = -3 m2 = 3

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

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Warm-up 1.Write the equation of the line that passes through the point (0,5) and has a slope of 4. 2.Find the slope of a line passing through (-3,6) and.

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