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Norm Ebsary March 14, 2007
MAE 6328: Multimedia Project Absolute Value Equations and
Translations1
MAE6328 Algebra Number Theory & Patterns Middle Grade Teachers
Multimedia Project #1
Absolute ValueEquations & Translations
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations2
Multimedia Project
Classroom Interactive Lesson
Review Absolute ValueUsing number line Parent Equation y = |x|
Classroom ActivitiesGraph with Paper & Pencil GeoGebra Dynamic Worksheet
Discover Translations
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations3
Multimedia Project
Absolute Value Introduction
Absolute Value- distance from zero on the number line.Distance is positive, so is absolute value!
Example: y = |-5| = 5 and y = |5| = 5
0 1 2 43 5 6 7-1-2-3-4-5-6-7
5 5
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations4
Multimedia Project
Absolute Value Graph Review
y = |x|m = rise/runm = -1,1CorrespondingPoints equal & opposite
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations5
Multimedia Project
Absolute Value Graphing
3 Steps to graph absolute value equationStep 1: Find the vertex- where the “V” is!Step 2: Create a table
Table values of x, with 1 less/more than vertexCalculate the y value based on these 3 values of x
Step 3: Graph absolute value from table
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations6
Multimedia ProjectAbsolute Value Class Example Step 1
Class Example using y = |x + 3| - 4Remember y = |mx + b| + c
Value of x at the vertex is –b/m = -3/1 = -3Value of y at the vertex is c = -4The x, y coordinate of vertex = (-b/m, c)
So the vertex is at (-3,-4)
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations7
Multimedia ProjectAbsolute Value Class Example Step 2
Start with the vertex (-3,-4) poin
tx y
A -3 -4
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations8
Multimedia ProjectAbsolute Value Class Example Step 2
Start with the vertex (-3,-4)
Now add the x values for 1 less
point
x y
C -4
A -3 -4
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations9
Multimedia ProjectAbsolute Value Class Example Step 2
Start with the vertex (-3,-4)
Now add the x values for 1 less
Add x value for 1 more
point
x y
C -4
A -3 -4
B -2
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations1
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Multimedia ProjectAbsolute Value Class Example Step 2
y = |x + 3| - 4– With x = -4,
y = -3
– With x = -2y = -3
point
x y
C -4 -3
A -3 -4
B -2 -3
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations1
1
Multimedia ProjectGraph Absolute Class Example Step 3
Plot points from table using Graph Paper
point
x y
C -4 -3
A -3 -4
B -2 -3
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations1
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Multimedia Project
Graph Absolute Value
Verify points from table with Graph
point
x y
C -4 -3
A -3 -4
B -2 -3
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations1
3
Multimedia Project
Additional Class Example
Lets graph y = |2x| + 5Remember to:
Find the Vertex (b/m, c)Create Table w/3 ValuesGraph from table
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations1
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Multimedia Project
Additional Class Example
y = |2x| + 5
Vertex = (-b/m,c) => (0,5)
point x y
C
A 0 5
B
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations1
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Multimedia Project
Additional Class Example
y = |2x| + 5
Vertex = (-b/m,c) => (0,5)
point x y
C -1
A 0 5
B
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations1
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Multimedia Project
Additional Class Example
y = |2x| + 5
Vertex = (-b/m,c) => (0,5)
point x y
C -1
A 0 5
B 1
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations1
7
Multimedia Project
Additional Class Example
y = |2x| + 5
Vertex = (-b/m,c) => (0,5)
point x y
C -1 7
A 0 5
B 1
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations1
8
Multimedia Project
Additional Class Example
y = |2x| + 5
Vertex = (-b/m,c) => (0,5)
point x y
C -1 7
A 0 5
B 1 7
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations1
9
Multimedia Project
Additional Class Example
Plot points from table using Graph Paper
point
x y
C -1 7
A 0 5
B 1 7 y = |2x| + 5
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations2
0
Multimedia Project
Additional Class Example
Plot points from table using Graph Paper
point
x y
C -1 7
A 0 5
B 1 7
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations2
1
Multimedia Project
GeoGebra Dynamic Worksheet
Translation Worksheet Slidersy = |mx + b| +
c– m for slope– b for y
intercept– c for offset
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations2
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Multimedia Project
Norm Ebsary MAE 6328 Multimedia ProjectMarch 14, 2007 Absolute Value Equations and Translations2
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Multimedia Project
The End
Questions?
