2 1 Using Transformations to Graph Bell Ringer

2 -1 Using Transformations to Graph Bell Ringer Quadratic Functions 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) For each function, evaluate f(– 2), f(0), and f(3). 3. f(x) = x 2 Where are we going ? + 2 x + 6 6; 6; 21 What does she want us to learn ? 4. f(x) = 2 x 2 – 5 x + 1 19; 1; 4 Holt Mc. Dougal Algebra 2

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

2 -1 Using Transformations to Graph Transformations: Quadratic Functions Reference in your textbook Vocabulary 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 Holt Mc. Dougal Algebra 2

2 -1 Using Transformations to Graph Exit Question 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 Holt Mc. Dougal Algebra 2

WRITE: Bell Ringer SLOPE INTERCEPT FORM OF AN EQUATION VERTEX FORM OF AN EQUATION STANDARD FORM OF AN EQUATION Challenge yourself to do without notes!

Example: Translating Quadratic Functions Use the graph of f(x) = x 2 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) = x 2 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.

Example Using the graph of f(x) = x 2 as a guide, describe the transformations and then graph each function. g(x) = x 2 – 5 Identify h and k. g(x) = x 2 – 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.

2 -1 Using Transformations to Graph Quadratic Functions BELL RINGER Using complete sentence(s), what does each indicate about parabola? 2 f(x) = a(x – h) + k Holt Mc. Dougal Algebra 2

Example Using the graph of f(x) = x 2 as a guide, describe the transformations and then graph each function. g(x) = x 2 – 5 Identify h and k. g(x) = x 2 – 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) = –x 2 + 6 x – 8 by using a x – 1 1 3 5 7 g(x)= –x 2 +6 x – 8 table. (x, g(x))

example 1 cont. Evaluate: g(x) = –x 2 + 6 x – 8 by using a table, and calculate the Slope(s).

VERTEX WHAT IS IT? ITS FORMULA? X=-b 2 a Y = f -b 2 a Open your textbooks to page 246 and follow along.

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

Vertex example, #2: (2. 75, -7. 12) Y = 2 X 2 -11 X + 8 x = -b 2 a x = - (-11) 2(2) X = 11 4 Y = f(x) 2 Y = 2(11/4) – 11(11/4) + 8 Y = -57 8

Vertex example, #3: (0. 3, -3. 55) Y = -5 X 2 +3 X – 4 x = -b 2 a x = - (3) 2(-5) X=3 10 Y = f(x) 2 Y = -5(3/10) + 3(3/10) - 4 Y = -71/20

Example 1 cont. Evaluate: g(x) = –x 2 + 6 x – 8 by using a table, and calculate the Slope(s), and Vertex.

Example 2, Lets Use a Table Evaluate: g(x) = x 2 + 3 x – 11 by using a table. x – 3 -1 -0 2 4 2 g(x)= x + 3 x – 11 (x, g(x))

Example 2 cont. Evaluate: g(x) = x 2 + 3 x – 11 by using a table, and calculate the Slope(s).

Example 2 cont. Evaluate: g(x) = x 2 + 3 x – 11 by using a table, and calculate the Slope(s), Vertex.

2 -1 Using Transformations to Graph Exit Question 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) = x 2 + 2 x + 6 6; 6; 21 2. f(x) = 2 x 2 – 5 x + 1 19; 1; 4 Holt Mc. Dougal Algebra 2

Bell Ringer Evaluate: g(x) = -x 2 + 2 x + 4 by using a table, and calculate the slope, and Vertex. x – 2 -1 0 1 2 g(x)= -x 2 +2 x +4 (x, g(x))

Example: Reflecting, Stretching, and Compressing Quadratic Functions Using the graph of f(x) = x 2 as a guide, describe the transformations and then graph each function. 1 g (x )= - x 4 2 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) = x 2 as a guide, describe the transformations and then graph each function. g(x) =(3 x)2 Because b = , g is a horizontal compression of f by a factor of.

ACTIVITY GROUP PRACTICE FINISH PAGES 40 -45 PACKET DUE NEXT CLASS

Exit Question Using the graph of f(x) = x 2 as a guide, describe the transformations, and then graph -1 g(x) = (x + 1)2. 5 g is f reflected across x-axis, vertically compressed by a 1 factor of 5 , and translated 1 unit left.