Warm Up #5

HW Check 22) y 0 24) x -2 26) w ≤ ½ and w ≥ -7/2 36) x = 16/3 or -14/3 38) X = 13/8 40) x = 11/8 42) X = -71/36 44) x ≤ 26/3 and x ≥ -6 46) All real numbers 48) all real numbers 50) x ≥ 48/5 or x ≤-42/5 52) x -5 Answers in red should have graphs included!

Pop Quiz! Clear your desk except for a pencil & calculator! You have 20 minutes to work!

2.5 – Absolute Value Graphs

Use a Graphing Calculator to graph the following, then answer questions in red  y = |x|  y = -|x| Graphing Instructions: y =  MATH  NUM  1.abs *What is the basic shape of these functions? *What do you think determines whether the graphs opens up or down? * What is the vertex of both functions?

1. y = -|x + 6| 2. y = | x – 6| + 3 Graphing Instructions: y =  MATH  NUM  1.abs Use a Graphing Calculator to graph the following, then identify the vertex.

Absolute Value Equations y = |mx + b| + k such that m ≠ 0

y = |mx + b| + k To find the vertex When describing an absolute value function, it is necessary to be able to give the vertex of the graph.

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

You Try! Find the vertex

Class work: Find the vertex of each graph using the calculator and determine whether it is a max or min 1. y = |x| y = |3x – 15|  y = |2x – 1| + 7  y = |9 – x| - 2 Calculator Instructions: 2 nd  CALC  MIN/MAX  LEFT  RIGHT  ENTER

2.6 Vertical and Horizontal Translations

Translations A TRANSLATION is an operation that shifts a graph horizontally, vertically, or both. The PARENT FUNCTION is the simplest function. Absolute Value Parent Function: 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 and y 3. y = |x| + 3 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. Graph these functions in y 2 and y 3 y = |x – 5| y = |x + 4| Describe the effect of h on the graph of y = |x – h|

Translations y = |x – h| + k is a translation (h) Units left or right (+ left, - right) (k) Units up or down (+ up, - down)

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

Practice Worksheet Absolute Value Crossword Puzzle

Homework Pg – 18 even all even Tutoring Thursday after school! Unit 1 Test – Friday!