Warm Up #5

HW Check 22) y < 18 and y > 0 24) x < 6 and 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 < 11 and 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

1.y = |x|

2.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 VertexFind the vertex of the equation:

Y = |x – 8| - 2

You Try! Find the vertex

y2x 4

Class work: Find the vertex of each graph using the calculator and determine whether

it is a max or min

1. y = |x| - 5

2. y = |3x – 15|

3. y = |2x – 1| + 7

4. y = |9 – x| - 2

Calculator Instructions: 2nd CALC MIN/MAX LEFT RIGHT ENTER

2.6 Vertical and Horizontal Translations

TranslationsA 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 y1

Step 2: Use your graphing calculator to graph each of these functions in the same viewing window using y2 and y3.

y = |x| + 3 y= |x| - 7

Describe the effect of k on the Graph of

y = |x| + k

Discovering TranslationsStep 3: Repeat step 2 for these functions. Keep y = |x| under y1.

Graph these functions in y2 and y3

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 TranslationsHorizontal 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

HomeworkPg 88-8910 – 18 even29-32 all34-44 even

Tutoring Thursday after school!

Unit 1 Test – Friday!