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