Holt McDougal Algebra 2

2-1 Using Transformations to Graph Quadratic Functions

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

1. 6 units down

2. 3 units right

(–2, –1)

(1, 5)

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

3. f(x) = x2 + 2x + 6

4. f(x) = 2x2 – 5x + 1

6; 6; 21

19; 1; 4

Where are we going ?

What does she want us to learn ?

Bell Ringer

f(x)= a(x – h) + k2

reflection across

the x-axis and / or a

vertical stretch or

compression.

Horizontal

translation

Vertical

translation

negative

Holt McDougal Algebra 2

2-1 Using Transformations to Graph Quadratic Functions

Quadratic FunctionQuadratic Function Parabola

Vertex of a Parabola Standard Form Vertex Form

Slope Intercept FormMaximum Value vs. Minimum Value

Vocabulary

Due test day

September 9, 2014

Test 2 Term 1

Reference in

your

textbook

Transformations: Quadratic Functions

Holt McDougal Algebra 2

2-1 Using Transformations to Graph Quadratic Functions

You either need to copy question or answer using complete sentences. If you copy question, you may use

bullets to answer.

Describe the path of a football that is kicked into the air.

Why?

Will the “h” or “k” be negative?

Hint: creating a graph might be helpful

Exit Question

WRITE:

SLOPE INTERCEPT FORM OF AN

EQUATION

VERTEX FORM OF AN EQUATION

STANDARD FORM OF AN EQUATION

Bell Ringer

Challenge yourself to do without notes!

Use the graph of f(x) = x2 as a guide, describe the transformations and then graph each function.

Example: Translating Quadratic Functions

g(x) = (x – 2)2 + 4

Identify h and k.

g(x) = (x – 2)2 + 4

h = 2, the graph is translated 2 units right. k = 4, the graph is translated 4 units up. g is f translated 2 units right and 4 units up.

h k

Use the graph of f(x) = x2 as a guide, describe the transformations and then graph each function.

Example: Translating Quadratic Functions

Because h = –2, the graph is translated 2 units left. Because k = –3, the graph is translated 3 units down. Therefore, g is f translated 2 units left and 4 units down.

h k

g(x) = (x + 2)2 – 3

Identify h and k.

g(x) = (x – (–2))2 + (–3)

Using the graph of f(x) = x2 as a guide, describe the transformations and then graph each function.

g(x) = x2 – 5

Identify h and k.

g(x) = x2 – 5

Because h = 0, the graph is not translated horizontally. Because k = –5, the graph is translated 5 units down. Therefore, g is f is translated 5 units down.

k

Example

Holt McDougal Algebra 2

2-1 Using Transformations to Graph Quadratic Functions

BELL RINGER

Using complete sentence(s), what does each indicate about parabola?

f(x) = a(x – h) + k 2

Using the graph of f(x) = x2 as a guide, describe the transformations and then graph each function.

g(x) = x2 – 5

Identify h and k.

g(x) = x2 – 5

Because h = 0, the graph is not translated horizontally. Because k = –5, the graph is translated 5 units down. Therefore, g is f is translated 5 units down.

k

Example

Lets Use a Table, example 1

Evaluate: g(x) = –x2 + 6x – 8 by using a table.

x g(x)= –x2 +6x –8 (x, g(x))

–1

1

3

5

7

example 1 cont.

Evaluate: g(x) = –x2 + 6x – 8 by using a table, and

calculate the Slope(s).

VERTEX

WHAT IS IT?

ITS FORMULA?

Open your textbooks to page 246 and follow along.

X = - b

2aY = f

-b

2a

Y = X -2X – 3

Vertex example, #1:

2

x = -b

2ax = - (-2)

2(1)

X = 1

Y = f(x)

Y = (1) – 2(1) - 32

Y = -4

(1, -4)

Y = 2X -11X + 8

Vertex example, #2:

2

x = -b

2ax = - (-11)

2(2)X = 11

4

Y = f(x)

Y = 2(11/4) – 11(11/4) + 82

Y = -57

8

(2.75, -7.12)

Y = -5X +3X – 4

Vertex example, #3:

2

x = -b

2ax = - (3)

2(-5)

X = 3

10

Y = f(x)Y = -5(3/10) + 3(3/10) -

4

2

Y = -71/20

(0.3, -3.55)

Example 1 cont.

Evaluate: g(x) = –x2 + 6x – 8 by using a table, and

calculate the Slope(s), and Vertex.

Example 2, Lets Use a Table

Evaluate: g(x) = x2 + 3x – 11 by using a table.

x g(x)= x + 3x – 11 (x, g(x))

–3

-1

-0

2

4

2

Example 2 cont.

Evaluate: g(x) = x2 + 3x – 11 by using a table, and calculate the Slope(s).

Example 2 cont.

Evaluate: g(x) = x2 + 3x –11 by using a table, and calculate the Slope(s), Vertex.

Holt McDougal Algebra 2

2-1 Using Transformations to Graph Quadratic Functions

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

Must show work in a table format for credit.

1. f(x) = x2 + 2x + 6

2. f(x) = 2x2 – 5x + 1

6; 6; 21

19; 1; 4

Exit Question

Bell Ringer

Evaluate: g(x) = -x2 + 2x + 4 by using a table, and calculate the slope, and Vertex.

x g(x)= -x2 +2x +4 (x, g(x))

–2

-1

0

1

2

Using the graph of f(x) = x2 as a guide, describe the transformations and then graph each function.

Example: Reflecting, Stretching, and Compressing Quadratic Functions

Because a is negative, g is a reflection of f across the x-axis.

Because |a| =- , g is a vertical compression of f by a factor of - .

g x 21

4x

Using the graph of f(x) = x2 as a guide, describe the transformations and then graph each function.

g(x) =(3x)2

Example: Reflecting, Stretching, and Compressing Quadratic Functions

Because b = , g is a horizontal compression of f by a factor of .

ACTIVITY GROUP PRACTICE

FINISH PAGES 40-45 PACKETDUE NEXT CLASS

Exit Question

Using the graph of f(x) = x2 as a guide, describe the transformations, and then graph

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

g is f reflected across x-axis, vertically compressed by a factor of , and translated 1 unit left.

-1

5

1

5