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Published byJordan Knight Modified over 8 years ago
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Unit 1: Chapter 2.5 and 2.6 Absolute Value Graphs, and Translations
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Use a Graphing Calculator to graph the follow. Y = |x| Y = -|x| Y = |x| + 3 Y = |x| - 3 Y = -|x + 6| Y = | x – 6| Graphing Instructions: Y = MATH NUM 1.abs
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Think about it! What shape is the graph of an absolute value functions? What determines the direction of the graph? (opening up or down?)
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Absolute Value Graphs F(x) = |MX + B| + K such that M ≠ 0 The VERTEX of a function is a point where the function reaches a MAXIMUM or MINIMUM.
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Finding the Vertex Find the vertex of the equation: Y = |x – 8| - 2
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Try some: Find the vertex of each graph and determine whether it is a max or min 1. Y = |x| - 5 2. Y = |3x – 15| Y = |x – 1| Y = |2x – 1| + 7 Y = |x + 3| Y = |9 – x| - 2 Calculator Instructions: 2 nd CALC MIN/MAX LEFTB RIGHTB ENTER
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Translations A TRANSLATION is an operation that shifts a graph horizontally, vertically, or both. The PARENT FUNCTION is the simplest function. Absolute Value: Y = |x|
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Discovering Translations Step 1: Graph Y = |x| under Y 1 Step 2: Use your graphing calculator to graph each of these functions in the same viewing window using Y 2, Y 3, and Y 4. Y = |x| + 3Y = |x| + 5 Y= |x| + 7 Describe the effect of K on the Graph of Y = |x| + K
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Discovering Translations Step 3: Repeat step 2 for these functions. Keep Y = |x| under Y 1. Y = |x – 5| Y = |x + 4|Y = |x – 2| Describe the effect of H on the graph of Y = |x – h|
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Translations Y = |x – h| + h is a translation!! (h) Units left of right (Opposite to sign) (k) Units up or down
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Types of Translations Horizontal Translation (left/right) |x ± h| Vertical Translation (up/down) |x| ± k Diagonal translation if it moves horizontally and vertically.
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