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Warm Up #5
HW Check 22) y < 18 and y > 0 24) x < 6 and x >
-2
26) w ≤ ½ and w ≥ -7/2 36) x = 16/3 or -14/3
38) X = 13/8 40) x = 11/8
42) X = -71/36 44) x ≤ 26/3 and x ≥ -6
46) All real numbers 48) all real numbers
50) x ≥ 48/5 or x ≤-42/5 52) x < 11 and x > -5
Answers in red should
have graphs included!
Pop Quiz!Clear your desk except for a
pencil & calculator!
You have 20 minutes to work!
2.5 – Absolute Value Graphs
Use a Graphing Calculator to graph the following, then answer questions in red
1.y = |x|
2.y = -|x|
Graphing Instructions:y = MATH NUM 1.abs
*What is the basic shape of these functions?
*What do you think determines whether the graphs opens up or down?
* What is the vertex of both functions?
1. y = -|x + 6| 2. y = | x – 6| + 3
Graphing Instructions:y = MATH NUM 1.abs
Use a Graphing Calculator to graph the following, then identify the vertex.
Absolute Value Equations
y = |mx + b| + k such that m ≠ 0
y = |mx + b| + k
To find the vertex
When describing an
absolute value
function, it is
necessary to
be able to give
the vertex of
the graph.
Finding the VertexFind the vertex of the equation:
Y = |x – 8| - 2
You Try! Find the vertex
y2x 4
Class work: Find the vertex of each graph using the calculator and determine whether
it is a max or min
1. y = |x| - 5
2. y = |3x – 15|
3. y = |2x – 1| + 7
4. y = |9 – x| - 2
Calculator Instructions: 2nd CALC MIN/MAX LEFT RIGHT ENTER
2.6 Vertical and Horizontal Translations
TranslationsA TRANSLATION is an operation that shifts a graph horizontally, vertically, or both.
The PARENT FUNCTION is the simplest function.
Absolute Value Parent Function: y = |x|
Discovering Translations
Step 1: Graph y = |x| under y1
Step 2: Use your graphing calculator to graph each of these functions in the same viewing window using y2 and y3.
y = |x| + 3 y= |x| - 7
Describe the effect of k on the Graph of
y = |x| + k
Discovering TranslationsStep 3: Repeat step 2 for these functions. Keep y = |x| under y1.
Graph these functions in y2 and y3
y = |x – 5| y = |x + 4|
Describe the effect of h on the graph of
y = |x – h|
Translations
y = |x – h| + k is a translation
(h) Units left or right (+ left, - right)
(k) Units up or down (+ up, - down)
Types of TranslationsHorizontal Translation (left/right)
|x ± h|
Vertical Translation (up/down)
|x| ± k
Diagonal translation if it moves horizontally and vertically.
Practice Worksheet Absolute Value Crossword
Puzzle
HomeworkPg 88-8910 – 18 even29-32 all34-44 even
Tutoring Thursday after school!
Unit 1 Test – Friday!
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