Unit 1: Chapter 2.5 and 2.6 Absolute Value Graphs, and Translations

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

Think about it! What shape is the graph of an absolute value functions? What determines the direction of the graph? (opening up or down?)

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.

Finding the Vertex Find the vertex of the equation: Y = |x – 8| - 2

Try some: Find the vertex of each graph and determine whether it is a max or min 1. Y = |x| 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

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|

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

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|

Translations Y = |x – h| + h is a translation!! (h) Units left of right (Opposite to sign) (k) Units up or down

Types of Translations Horizontal Translation (left/right) |x ± h| Vertical Translation (up/down) |x| ± k Diagonal translation if it moves horizontally and vertically.