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6-8: Graphing Absolute Value Equations

6-8: Graphing Absolute Value Equations. Objective: To graph absolute value equations by using translation. Absolute Value Equations . ACTIVITY Graph: y = IxI Now, graph: y = IxI + 2 Describe how the graphs are the same and how they are different. Translation.

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6-8: Graphing Absolute Value Equations

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  1. 6-8: Graphing Absolute Value Equations Objective: To graph absolute value equations by using translation

  2. Absolute Value Equations • ACTIVITY • Graph: y = IxI • Now, graph: y = IxI + 2 • Describe how the graphs are the same and how they are different.

  3. Translation • = a shift of a graph horizontally, vertically, or both. The result is a graph of the same shape and size, but different position.

  4. Vertical Translation • A shift of the absolute value equation up or down. • The graph of y = IxI + k is a translation of the graph y = IxI. Let k be a positive number. So, y = IxI + k translates the graph of y = IxI up k units while y = IxI-k translates the graph of IxI down k units.

  5. Practice Vertical Translation • Graph: • y = IxI + 4 • y = IxI – 5

  6. Horizontal Translation • Translation left and right • For a positive number h, y = Ix + hI translates the graph of y = IxI by h units to the left and y = Ix – hI translates the graph of y = IxI by h units to the right

  7. Practice horizontal translation • y = Ix-4I • y = Ix+1I • y = Ix+8I • y = Ix-6I • Write an equation for each translation: • 5 units right 7 units left 3 units up

  8. Homework • P361-362 #1-35 ALL

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