Transcript Slide 1
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) = x2 Where are we going ? + 2x + 6 6; 6; 21 What does she want us to learn ? 4. f(x) = 2x2 – 5x + 1 19; 1; 4 Holt McDougal Algebra 2 Horizontal translation 2 f(x)= a(x – h) Vertical +k translation reflection across the x-axis and / or a vertical stretch or compression. negative 2-1 Using Transformations to Graph Transformations: Quadratic Functions 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 McDougal 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 McDougal 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) = 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. 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. 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 McDougal Algebra 2 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 x –1 1 3 5 7 g(x)= –x2 +6x –8 table. (x, g(x)) example 1 cont. Evaluate: g(x) = –x2 + 6x – 8 by using a table, and calculate the Slope(s). VERTEX WHAT IS IT? ITS FORMULA? X=-b 2a Y = f -b 2a Open your textbooks to page 246 and follow along. Vertex example, #1: (1, -4) Y = X 2 -2X – 3 x = -b 2a 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 = 2X2 -11X + 8 x = -b 2a 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 = -5X2 +3X – 4 x = -b 2a 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) = –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 –3 -1 -0 2 4 g(x)= x 2 + 3x – 11 (x, g(x)) 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. 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) = x2 + 2x + 6 6; 6; 21 2. f(x) = 2x2 – 5x + 1 19; 1; 4 Holt McDougal Algebra 2 Bell Ringer Evaluate: g(x) = -x2 + 2x + 4 by using a table, and calculate the slope, and Vertex. x –2 -1 0 1 2 g(x)= -x2 +2x +4 (x, g(x)) 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 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) = 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 . 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 -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.