2.1­Using Transformations to Graph Quadratic Functions.notebook

1

December 11, 2013

Sep 16­12:50 PM

Warm­Up

For each translation of the point (­2, 5), give the coordinates of the translated point.

1. 6 units down

2. 3 units right

For each function, evaluate f(­2), f(0), and f(3).

3. f(x)=x+2x+6

4. f(x)=2x­5x+12

2

2.1­Using Transformations to Graph Quadratic Functions.notebook

2

December 11, 2013

Sep 16­12:42 PM

Unit 2­Quadratic Functions 

2.1­Using Transformations to Graph Quadratic Functions.notebook

3

December 11, 2013

Sep 16­12:53 PM

Linear vs. Quadratic

2.1­Using Transformations to Graph Quadratic Functions.notebook

4

December 11, 2013

Sep 16­12:44 PM

A quadratic function is a function that can be written in the form f(x)=a(x­h)+k (a=0).2 /

Characteristics of a Quadratic Functions

1. The variable is always squared

2. Shape of the graph is a parabola

2.1­Using Transformations to Graph Quadratic Functions.notebook

5

December 11, 2013

Sep 16­12:53 PM

Example 1: Graphing Quadratic Functions Using a Table

Graph f(x)=x-6x+8 by using a table.

Make a table. Plot enough ordered pairs to see both sides of the curve.

2

x f(x)=x -6x+8 (x, f(x))2

2.1­Using Transformations to Graph Quadratic Functions.notebook

6

December 11, 2013

Sep 16­12:53 PM

Example 2: Graphing Quadratic Functions Using a Table

Graph f(x)=x-4x+3 by using a table.

Make a table. Plot enough ordered pairs to see both sides of the curve.

2

x f(x)=x -4x+3 (x, f(x))2

YOU TRY!

2.1­Using Transformations to Graph Quadratic Functions.notebook

7

December 11, 2013

Sep 17­2:25 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

8

December 11, 2013

Sep 16­1:02 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

9

December 11, 2013

Sep 20­12:41 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

10

December 11, 2013

Sep 20­12:42 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

11

December 11, 2013

Sep 20­8:46 AM

2.1­Using Transformations to Graph Quadratic Functions.notebook

12

December 11, 2013

Sep 20­12:43 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

13

December 11, 2013

Sep 20­12:45 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

14

December 11, 2013

Sep 20­12:46 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

15

December 11, 2013

Sep 20­1:06 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

16

December 11, 2013

Sep 20­1:11 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

17

December 11, 2013

Sep 20­1:15 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

18

December 11, 2013

Sep 20­1:18 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

19

December 11, 2013

Sep 20­8:48 AM

2.1­Using Transformations to Graph Quadratic Functions.notebook

20

December 11, 2013

Sep 20­8:50 AM

2.1­Using Transformations to Graph Quadratic Functions.notebook

21

December 11, 2013

Sep 20­8:55 AM

2.1­Using Transformations to Graph Quadratic Functions.notebook

22

December 11, 2013

Sep 20­9:16 AM

2.1­Using Transformations to Graph Quadratic Functions.notebook

23

December 11, 2013

Sep 20­9:22 AM

2.1­Using Transformations to Graph Quadratic Functions.notebook

24

December 11, 2013

Sep 20­9:27 AM

2.1­Using Transformations to Graph Quadratic Functions.notebook

25

December 11, 2013

Sep 16­2:25 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

26

December 11, 2013

Sep 16­2:26 PM

Warm-Up

Using the graph f(x)=x as a guide, describe the transformations, and then graph each function.

1. g(x)=x -5

2. g(x)=(x+3) -2

3. g(x)=x+2x-1

2

2

2

USE A T­CHART TO GRAPH #3

2

2.1­Using Transformations to Graph Quadratic Functions.notebook

27

December 11, 2013

Sep 23­11:02 AM

Test Corrections1. You must make the corrections on a separate sheet of paper.

2. You may use your notes, classwork, or textbook

3. You may work with one other person (no more than 2 per group!)

4. You MUST show work to receive credit back

2.1­Using Transformations to Graph Quadratic Functions.notebook

28

December 11, 2013

Sep 20­2:42 PM

Practice Sheet for Graphing Quadratics Using a Chart1. You must make a t­chart for each graph

2. Fill in the t­chart completely before graphing

3. You may work with a partner, but you will turn in your work individually

Get the sheet out from last class and complete!!

2.1­Using Transformations to Graph Quadratic Functions.notebook

29

December 11, 2013

Sep 25­1:48 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

30

December 11, 2013

Sep 20­2:51 PM

Discuss Chart From Book

2.1­Using Transformations to Graph Quadratic Functions.notebook

31

December 11, 2013

Sep 19­1:42 PM

Warm­Up1. Graph f(x)=x

2. Graph f(x)=(1/4)x

3. Describe the 

   transformation

2

2

2.1­Using Transformations to Graph Quadratic Functions.notebook

32

December 11, 2013

Sep 19­1:42 PM

Example1. Graph f(x)=x

2. Graph f(x)=4x

3. Describe the 

   transformation

2

2

2.1­Using Transformations to Graph Quadratic Functions.notebook

33

December 11, 2013

Sep 16­2:31 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

34

December 11, 2013

Sep 24­1:57 PM

Practice

Page 64 #8­13

2.1­Using Transformations to Graph Quadratic Functions.notebook

35

December 11, 2013

Sep 19­2:30 PM

Writing Assignment #2Describe the similarities and differences between a linear function and a quadratic function. Give specific details.

How did you study for the Unit 1 Test? How much time did you spend studying? Explain how you might study differently for the Unit 2 Test. 

2.1­Using Transformations to Graph Quadratic Functions.notebook

36

December 11, 2013

Sep 16­2:35 PM

Using the graph f(x)=x as a guide, describe the transformations, and then graph each function.

1. g(x)=2x

2. g(x)=1/2x

2

2

2

Warm­up

2.1­Using Transformations to Graph Quadratic Functions.notebook

37

December 11, 2013

Sep 30­10:12 AM

Graph the Following:

1. f(x)=x

2. f(x)=1/4x

3. f(x)=4x

2

2

2

2.1­Using Transformations to Graph Quadratic Functions.notebook

38

December 11, 2013

Sep 16­2:37 PM

Vertex

If a parabola opens upward, it has a lowest point. If a parabola opens downward, it has a highest point. The lowest or highest point is the vertex of a parobola.

2.1­Using Transformations to Graph Quadratic Functions.notebook

39

December 11, 2013

Sep 16­2:37 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

40

December 11, 2013

Sep 30­10:14 AM

Find the Vertex of the following function

1. f(x)= (x­3)+5

2. f(x)=­(x+4)­22

2

2.1­Using Transformations to Graph Quadratic Functions.notebook

41

December 11, 2013

Sep 16­2:39 PM

Writing Transformed Quadratic FunctionsUse the description to write the quadratic function in vertex form. The parent function f(x)=x is reflected across the x-axis, vertically stretched by a factor of 6, and translated 3 units left to create g.

Step 1: Identify how each transformation affects the constants in vertex form.

reflection across x-axis:

vertical stretch by 6:

translation left 3 units:

Step 2: Write the transformed function.

2

2.1­Using Transformations to Graph Quadratic Functions.notebook

42

December 11, 2013

Sep 16­2:43 PM

You try!

1. The parent function f(x)=x is vertically compressed by a factor of 1/3 and translated 2 units right and 4 units down to create g.

2. The parent function f(x)=x is reflected across the x-axis and translated 5 units left and 1 unit up to create g.

2

2

2.1­Using Transformations to Graph Quadratic Functions.notebook

43

December 11, 2013

Sep 16­2:46 PM

Practice

Page 64 #'s 1,8-13, 29, 30

2.1­Using Transformations to Graph Quadratic Functions.notebook

44

December 11, 2013

Sep 17­11:07 AM

Writing Assignment #2

Reflect on your experience in this classroom. What have you found challenging? What concepts are you confident about? Explain.

2.1­Using Transformations to Graph Quadratic Functions.notebook

45

December 11, 2013

Sep 24­1:58 PM

2.1­Using Transformations to Graph Quadratic Functions.notebook

46

December 11, 2013

Sep 26­8:13 AM

2.1­Using Transformations to Graph Quadratic Functions.notebook

47

December 11, 2013

Sep 26­10:49 AM

2.1­Using Transformations to Graph Quadratic Functions.notebook

48

December 11, 2013

Sep 26­10:54 AM

2.1­Using Transformations to Graph Quadratic Functions.notebook

49

December 11, 2013

Sep 30­10:11 AM