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6.7 Graphing Absolute Value Equations 3/3/08 A V-shaped graph that points upward or downward is the graph of an absolute value equation. A translation is a shift of a graph vertically, horizontally, or both. –The result is a graph of the same shape and size, but in a different location.

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Vertical Translations Below are the graphs of y = | x | and y = | x | + 2. Describe how the graphs are the same and how they are different. y = | x |y = | x | + 2

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Vertical Translations The graphs are the same shape. The y – intercept of the first graph is 0. The y – intercept of the second graph is 2. The graph moved up two places on the y – axis, but stayed the same shape.

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Graphing a Vertical Translation Graph y = | x | - 1. Start with the graph of y = | x |. Translate the graph down 1 unit. y = | x | - 1 y = | x |

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Writing an Absolute Value Equation Write an equation for each translation of y = | x |. a.8 units down. The equation is y = | x | - 8. b.6 units up. The equation is y = | x | + 6.

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Graphing a Horizontal Translation Graph each equation by translating y = | x |. a.y = | x + 2 | b.y = | x – 2 | y = | x | y = | x + 2 | y = | x | y = | x - 2 |

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More Practice!!!! Textbook – p. 327 – 328 # 2 – 34 even. Homework – Worksheet 6.7

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