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Name: Date: Period: Topic: Graphing Absolute Value Equations Warm-Up: 1. Solve the following system of inequalities by graphing: y < 2x + 4 - 3x – 2y ≥ 6 2. Which inequality represents the graph below? a) y < x + 1 b) y ≥ x + 1 c) y ≤ x + 1 d) y > x + 1 Home-Learning Assignment #5 Review Quiz #8 Graphing Absolute Value Equations How do I make one of those V graphs? Absolute value transformation Vocabulary: Translation: shifts the parent function graph horizontally and vertically. Reflection: it creates a mirror image of the parent-function graph across the line of reflection. Parent Function y = │x │ Vertical Movements? Absolute value rules: If you have minus outside the absolute value, you move down on the coordinate plane. y =│x│- 2 If you have addition outside the absolute value, you move up on the coordinate plane. y =│x│+ 2 Lets practice! y = │x│ - 4 y = │x│+ 3 Your turn! y = │x│ + 7 y = │x│ - 2 Horizontal Movements? Absolute value special rules: If you have minus inside the absolute value, you move to the right on the coordinate plane. y =│x - 2 │ If you have addition inside the absolute value, you move to the left on the coordinate plane. y =│x + 2 │ Lets Practice! y =│x - 5│ y =│x + 6│ Your Turn! y =│x + 4│ y =│x - 1│ What about y = │x - 4 │+ 5 What about y = -│x - 2 │ y = -│x │ Reflection of the Parent-function Same rule, but now it makes it look down Practice Time!!! Algebra Aerobics! 1) y = │x - 1│ 6) y = │x - 1│+ 2 2) y = │x +3│ 7) y = -│x - 6│ 3) y = │x │ + 5 8) y = -│x │- 4 4) y = │x│ - 4 9) │x│+ y = - 3 5) y = │x + 3│ + 3 10) y = -│x + 1│ - 1 Mix Algebra Aerobics y = │x - 4│ y = -│x + 2│ - 2 y ≥ -3x -1 y = -│x - 7│ + 8 y = │x + 5│ x≥4 y≥6 4x + 3y ≤ 24 y = │x │ + 3 Review Review Review Verbal Comprehension Analysis Graph the functions y = │x │ and y = │x - 3 │ together on the same coordinate plane. What effect does the 3 have on the graph? Graph the functions y = │x │ and y = │x │- 3 on the same coordinate plane. What effect does the 3 have on the graph? Graph the functions y = │x │ and y = - │x │ together on a coordinate plane. What effect does the negative sign have on the graph? Wrap-up: Review key points Review vocabulary words ---- Reminder ---Study for Exam #8 (Linear Inequalities, Systems of Inequalities, & Graphing Absolute Value Equations)