QUIZ: Complete on graph paper: Given y = x2 + 6x + 8 find algebraically: The axis of symmetry The vertex (as an ordered pair) The solutions (x-intercepts) The y-intercept (as an ordered pair) After you find the above, graph the quadratic The axis of symmetry: x = -3 The vertex: (-3, -1) The solutions (x-intercepts): x = -2 or x = -4 The y-intercept: (0, 8)

SWBAT… investigate transformations of quadratic functions. Mon, 5/16 Agenda WU (5 min) Roots conclusions (5 min) TI-83 Graphing calculator investigation activity (30 min) WARM-UP 1. Write your hw in your planners 2. Take out hw#2 3. In baseball, a pop fly should be easily caught if it stays in the air for 7 seconds. Suppose a ball that is hit can be represented by the function y = –16t2 + 125t + 5, where y is the height after t seconds. Will the ball be considered an easy catch? (Hint: use the graphing calculator) HW#3: Short Response – see agenda Yes, because t > 7

3 Types of Solutions Two real roots Double root No real roots

Graphing Calculator Activity: Transformations Each pair will be given a TI-83 You will be answering the questions on your worksheet that deal with the transformations of quadratics You will be investigating three types of transformations Vertical Translations Dilations Reflections You have the class period today to finish this! HW: One Short response questions: see agenda (due Wednesday)

SWBAT… complete the square. Thurs, 5/19 Agenda WU (10 min) Transformations (10 min) Completing the square (20 min) WARM-UP 1. In your tables, switch HW3-short response clockwise 2. Write comments on the paper you have. -Did they describe two graph differences? -Did they explain each difference? HW#4: Completing the square

Sample Correct Response The graph of y = 4x2 will be narrower than the graph of y = x2 – 3 because the coefficient of 4x2 is larger. The graph of y = x2 – 3 is lower because the -3 shifts the graph down 3 units. Scoring Guidelines 2: The response provides two ways the graphs are different, along with an adequate explanation of each difference. 1: The response provides evidence of understanding. For example, the response may: Include only one correct way the graphs are different, with an adequate explanation. Include two ways the graphs are different, with little or no explanation. 0: Response is incorrect or irrelevant. Include only incorrect ways the graphs are different, with no explanation. Restate the information provided in the item. Give irrelevant information.

Transformations Conclusions Vertical Translation: The constant is where the parabola will cross the y-axis. For example, y = x2 – 8 crosses the y-axis at -8 Dilation: The higher the value of a, the narrower the parabola For example, y = 6x2 is narrower than y = x2 The smaller the value of a, the wider the parabola For example, y = 1/2x2 is wider than y = x2 Reflection: If a is negative the parabola is reflected across the x-axis. For example, y = -x2 + 2 is reflected across the x-axis (upside down u)

Describe how the graph of the function g(x) = x2 – 2 is related to the graph of f(x) = x2. A.) The graph is a translation left 2 units from f(x). B.) The graph is a translation right 2 units from f(x). C.) The graph is a translation up 2 units from f(x). D.) The graph is a translation down 2 units from f(x).

This is the graph of the function g(x) = 1/2x2 This is the graph of the function g(x) = 1/2x2. Describe how it is related to the graph of f(x) = x2. Answer: The graph is stretched horizontally (wider) compared to f(x) = x2

QUIZ: Complete on a separate sheet of paper. Be Specific! Write neatly! Dave graphs the functions y = 1/4x2 and y = x2 + 2 on the same set of coordinate axes. State two ways the graphs are different. Explain the reason for each difference.

Completing the square is another method used to solve for quadratic equations. Work on HW#4- Completing the square (read and follow the example first!) Answers: x = -3 or x = -7 x = -0.4 or x = -5.6 x = 11.2 or x = -0.2 x = 0.5 or x = -2.5

Sample Correct Response The graph of y = 1/4x2 will be wider than the graph of y = x2 + 2 because the coefficient of 1/4x2 is smaller. The graph of y = x2 + 2 is two units higher because the 2 shifts the graph up 2 units. Scoring Guidelines 2: The response provides two ways the graphs are different, along with an adequate explanation of each difference. 1: The response provides evidence of understanding. For example, the response may: Include only one correct way the graphs are different, with an adequate explanation. Include two ways the graphs are different, with little or no explanation. 0: Response is incorrect or irrelevant. Include only incorrect ways the graphs are different, with no explanation. Restate the information provided in the item. Give irrelevant information.