Norm Ebsary March 14, 2007 MAE 6328: Multimedia Project Absolute Value Equations and Translations 1 MAE6328 Algebra Number Theory & Patterns Middle Grade Teachers Multimedia Project #1 Absolute Value Equations & Translations

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 2 Classroom Interactive Lesson Review Absolute Value Using number line Parent Equation y = |x| Classroom Activities Graph with Paper & Pencil GeoGebra Dynamic Worksheet Discover Translations

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 3 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| =

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 4 Absolute Value Graph Review y = |x| m = rise/run m = -1,1 Corresponding Points equal & opposite

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 5 Absolute Value Graphing 3 Steps to graph absolute value equation Step 1: Find the vertex- where the “V” is! Step 2: Create a table Table values of x, with 1 less/more than vertex Calculate the y value based on these 3 values of x Step 3: Graph absolute value from table

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 6 Absolute Value Class Example Step 1 Class Example using y = |x + 3| - 4 Remember y = |mx + b| + c Value of x at the vertex is –b/m = -3/1 = -3 Value of y at the vertex is c = -4 The x, y coordinate of vertex = (-b/m, c) So the vertex is at (-3,-4)

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 7 Absolute Value Class Example Step 2 Start with the vertex (-3,-4) pointxy A-3-4

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 8 Absolute Value Class Example Step 2 Start with the vertex (-3,-4) Now add the x values for 1 less pointxy C-4 A-3-4

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 9 Absolute 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 pointxy C-4 A-3-4 B-2

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 10 Absolute Value Class Example Step 2 y = |x + 3| - 4 – With x = -4, y = -3 – With x = -2 y = -3 pointxy C-4-3 A -4 B-2-3

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 11 Graph Absolute Class Example Step 3 Plot points from table using Graph Paper pointxy C-4-3 A -4 B-2-3

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 12 Graph Absolute Value Verify points from table with Graph pointxy C-4-3 A -4 B-2-3

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 13 Additional Class Example Lets graph y = |2x| + 5 Remember to: Find the Vertex (b/m, c) Create Table w/3 Values Graph from table

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 14 Additional Class Example y = |2x| + 5 Vertex = (-b/m,c) => (0,5) pointxy C A05 B

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 15 Additional Class Example y = |2x| + 5 Vertex = (-b/m,c) => (0,5) pointxy C A05 B

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 16 Additional Class Example y = |2x| + 5 Vertex = (-b/m,c) => (0,5) pointxy C A05 B1

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 17 Additional Class Example y = |2x| + 5 Vertex = (-b/m,c) => (0,5) pointxy C7 A05 B1

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 18 Additional Class Example y = |2x| + 5 Vertex = (-b/m,c) => (0,5) pointxy C7 A05 B17

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 19 Additional Class Example Plot points from table using Graph Paper pointxy C7 A05 B17 y = |2x| + 5

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 20 Additional Class Example Plot points from table using Graph Paper pointxy C7 A05 B17

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 21 GeoGebra Dynamic Worksheet Translation Worksheet Sliders y = |mx + b| + c – m for slope – b for y intercept – c for offset

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 22

Multimedia Project Norm Ebsary MAE 6328 Multimedia Project March 14, 2007 Absolute Value Equations and Translations 23 The End Questions?