6.7 Graphing Absolute Value Equations. Vertical Translations Below are the graphs of y = | x | and y = | x | + 2. Describe how the graphs are the same.

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Presentation transcript:

6.7 Graphing Absolute Value Equations

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

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.

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 |

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

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 |

Writing an Absolute Value Equation Write an equation for each translation of y = | x |. a.4 units right. b.3 units left.

Graph the following equations. y = | x – 2 |

Graph the following equations. y = |x| - 2

Graph the following equations. y = | x + 3 |

More Practice!!!! Homework - Textbook p. 327 – 328 # 2 – 26 even