What does she want us to learn ? Bell Ringer For each translation of the point (–2, 5), give the coordinates of the translated point. 1. 6 units down (–2, –1) 2. 3 units right (1, 5) Where are we going ? What does she want us to learn ? For each function, evaluate f(–2), f(0), and f(3). 3. f(x) = x2 + 2x + 6 6; 6; 21 4. f(x) = 2x2 – 5x + 1 19; 1; 4

Horizontal translation f(x)= a(x – h) + k 2 reflection across the x-axis and / or a vertical stretch or compression. Vertical translation negative

Objectives F-IF.4, F-IF.6, F-IF.7a Transformations: Quadratic Functions Objectives F-IF.4, F-IF.6, F-IF.7a Transform quadratic functions. Describe the effects of changes in the coefficients of y = a(x – h)2 + k. up down Define, identify, and graph quadratic functions. Identify and use maximums and minimums of quadratic functions to solve problems. left right always negative *part of formula (-) (-) = (-) (+) =

Vocabulary Quadratic Function Parabola Vertex of a Parabola Transformations: Quadratic Functions Vocabulary Reference in your textbook Quadratic Function Parabola Vertex of a Parabola Standard Form Vertex Form Slope Intercept Form Maximum Value vs. Minimum Value Due test day September 9, 2014 Test 2 Term 1

Teaching note Watch 2-1 video, part 1 2) ***Copy Lab Activities softbook page 8, due next class; Allow enough time to complete 3) 3) Play video 2-1, part 2, just watch; tell students will watch tomorrow and take notes

Describe the path of a football that is kicked into the air. Why? Exit Question 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

Challenge yourself to do without notes! Bell Ringer Write: Slope Intercept Form of an Equation Vertex Form of an Equation Standard Form of an Equation Challenge yourself to do without notes!

2-1 video, part 2, do again today with pausing Teaching note 2-1 video, part 2, do again today with pausing Pause(s) .22, pointing out this is given; .36 and ask students how he knows h = -1 (negative in equation and (-)(-) = given +1) 2.01 so students have the option to write down new function 2.25 and ask students why he added a + in front of K? (part of formula)

Example: Translating Quadratic Functions Use the graph of f(x) = x2 as a guide, describe the transformations and then graph each function. g(x) = (x – 2)2 + 4 Identify h and k. g(x) = (x – 2)2 + 4 h k 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.

Example: Translating Quadratic Functions Use the graph of f(x) = x2 as a guide, describe the transformations and then graph each function. g(x) = (x + 2)2 – 3 Identify h and k. g(x) = (x – (–2))2 + (–3) h k 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.

Teaching note On next slide point out the 5 is not squared with (), so it cannot be the h

Example 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 k 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.

Using complete sentence(s), what does each indicate about parabola? Bell Ringer Using complete sentence(s), what does each indicate about parabola? 2 f(x) = a(x – h) + k

Example 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 k 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.

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? Y = f X = - b 2a -b 2a Open your textbooks to page 246 and follow along.

(1, -4) x = -b 2a x = - (-2) 2(1) Y = f(x) Y = (1) – 2(1) - 3 Y = -4 Vertex example, #1: Y = x -2x – 3 2 Y = f(x) x = -b 2a 2 Y = (1) – 2(1) - 3 x = - (-2) 2(1) Y = -4 X = 1

(2.75, -7.12) x = -b 2a x = - (-11) 2(2) Y = f(x) Vertex example, #2: Y = 2x -11x + 8 2 Y = f(x) x = -b 2a 2 Y = 2(11/4) – 11(11/4) + 8 x = - (-11) 2(2) Y = -57 8 X = 11 4

(0.3, -3.55) x = -b 2a x = - (3) 2(-5) Y = f(x) Vertex example, #3: Y = -5x +3x – 4 2 Y = f(x) x = -b 2a 2 Y = -5(3/10) + 3(3/10) - 4 x = - (3) 2(-5) Y = -71/20 X = 3 10

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. 2 x g(x)= x + 3x – 11 (x, g(x)) –3 -1 -0 2 4

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.

***MUST COPY ***soft Common Core workbook pages 40-45. Teaching note Application Activity You are welcome to work with your peers, but each of you will turn in your own paper. ***MUST COPY ***soft Common Core workbook pages 40-45. This is not homework; will continue to work on packet tomorrow in class.

Exit Question 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 6; 6; 21 2. f(x) = 2x2 – 5x + 1 19; 1; 4

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 1 2

Example: Reflecting, Stretching, and Compressing Quadratic Functions Using the graph of f(x) = x2 as a guide, describe the transformations and then graph each function. 1 ( ) g x = - x 2 4 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 - .

Example: Reflecting, Stretching, and Compressing Quadratic Functions Using the graph of f(x) = x2 as a guide, describe the transformations and then graph each function. g(x) =(3x)2 Because b = , g is a horizontal compression of f by a factor of .

Teaching note next slide Students already copied next slide, now they need to understand it Students need to be able to know if it is the a or b, being changed. Ask students how do they know if it is the a or b being changed? They should see it is an a value when x only squared; it is a b value when there are ( ) squared.

Activity Group practice finish pages 40-45 packet due 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. -1 5 g is f reflected across x-axis, vertically compressed by a factor of , and translated 1 unit left. 1 5