4AB CH 2­7 Absolute Value Graphs NOTES.notebook
September 16, 2014
CH 2.7 Absolute Value Functions and Graphs
Absolute value means ______________________________________
If |x|=3; then x=____ or _____
Do 1st page, pg 50
of CH 2.7 Student Companion.
A function in the form y=a|x­h|+k is an absolute value function. The graph will ALWAYS make a V with the vertex of the V at (h,k). Given y=2|x­3|­1; a=2, h=­3, and k=­1
1. Identify vertex (h,k): ______
2. Make a table,
plot several points
x | y
on both sides of vertex.
2. Plot the vertex and points from the table. CH 2-7 (pg 110 of text book)
General Form of the Absolute Value Function: y = a |x-h| + k
• a is the vertical stretch/compression factor (slope of the 2 lines)
• h is the horizontal shift (left/right)
• k is the vertical shift (up/down)
• The vertex is (h,k)
• The axis of symmetry is x = h
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4AB CH 2­7 Absolute Value Graphs NOTES.notebook
September 16, 2014
EXAMPLE 1 Graph
1.
3.
1.
2.
4.
1
2
Y=|x| Vertex:
axis of symmetry:
PARENT FUNCTION
2.
y=|x| +2 Vertex:
axis of symmetry:
Translation of parent:
3.
y=|x-4| +2 Vertex:
axis of symmetry:
2 translations:
4.
y=(1/2)|x-4| +2 Vertex:
axis of symmetry:
3 translations:
TABLE: x
y
Example 2 - You try: Which of the following is the graph of
y = |x + 3| -1 ?
Vertex:
Axis of symmetry:
Transformations:
You try - Do GOT IT? #'s 8-11 pg 51 of your CH 2.7
Student Companion.
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4AB CH 2­7 Absolute Value Graphs NOTES.notebook
September 16, 2014
Example 3a: What is the graph of y = -2 |x|?
Vertex:
Axis of symmetry:
Translation:
What characteristic of the
equation results in the V opening
downward?
Example 3b: What is the graph of y = -1/4 |x|?
Vertex:
Axis of symmetry:
Translation:
You try - Do GOT IT? problem 3 #'s 12-14 pg 52 of your
CH 2.7 Student Companion.
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4AB CH 2­7 Absolute Value Graphs NOTES.notebook
September 16, 2014
Example 4: Compare y = -2 |x + 2| +3 with the parent
function y = |x|. Without graphing, what are the vertex,
axis of symmetry, and transformations of the parent
function?
vertex:
axis of symmetry:
Transformations:
You try - Do GOT IT? problem 4 #'s 15-19 pg 53 of your
CH 2.7 Student Companion.
Example 5: What is the equation of the absolute value function?
STEP 1: Identify the vertex.
(h,k) = (___, ____)
STEP 2: Identify a.
What is the slope of
branch on right? ______
That is a!
STEP 3: Write the equation. Use y=a|x­h|+k; vertex is at (h,k) and a is the slope of the right branch of the V (stretch,compression)
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4AB CH 2­7 Absolute Value Graphs NOTES.notebook
September 16, 2014
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