1. Warm Up In previous courses, you have investigated linear and exponential functions. In this chapter, you will study quadratic functions. You will learn all you can about the graphs of quadratic functions and fully describe their features. The graph of a quadratic function has the shape of a parabola. In this lesson, you will learn about this shape. 5-1. FUNCTIONS OF AMERICA Congratulations! You have just been hired to work at a national corporation called Functions of America. Recently your company has had some growing pains, and your new boss has turned to your team for help. See her memo below. MEMO To: Your study team From: Ms. Freda Function, CEO Re: New product line I have heard that while lines and exponential curves are very popular, there is a new craze in Europe to have U-shaped designs. I recently visited Paris and Milan and discovered that we are behind the times! Please investigate this new function, which is called a quadratic function. The equation for a quadratic function can be written in the form y = ax 2 + bx + c, and the U-shaped graph is called a parabola. I’d like a full report at the end of today with any information your team can give me about parabolas. Spare no detail! I’d like to know everything you can tell me about the features of these graphs. I’d also like to know about any special points on a parabola or any patterns that exist in its table. Remember, the company is only as good as its employees! Your research is essential for the success of our new product line. Sincerely, Ms. Function, CEO

2. 5.1.1 Investigating the Graphs of Quadratic Functions January 13, 2016

3. Objectives CO: SWBAT investigate graphs of quadratic functions, learning about their shape and key features. LO: SWBAT describe the graphs of quadratic functions using appropriate vocabulary.

4. a. y = x 2 − 2x − 8b. y = −x 2 + 4 c. y = x 2 − 4x + 5d. y = x 2 − 2x + 1 e. y = x 2 − 6x + 5 f. y = −x 2 + 3x + 4 g. y = −x 2 + 2x − 1h. y = x 2 + 5x + 1 i. y = x 2 − 2x – 15j. y = –x 2 + 4x – 5 Red Yellow Orange Green Pink Table Blue Stripes Purple

5. j. y = –x 2 + 4x – 5 x01 y Attributes Shape: Vertex: Max/Min y-intercept: (0, ) Open up/down Domain: Range: x-intercepts: Line of symmetry: Graph Equation (2,-1) Parabola -10-5 -2 2 3 -2 4 -5 {all real numbers} None x = 2 GROUP COLOR

6. 5.1.1 Investigating the Graphs of Quadratic Functions January 14, 2016

7. Objectives CO: SWBAT investigate graphs of quadratic functions, learning about their shape and key features. LO: SWBAT describe the graphs of quadratic functions using appropriate vocabulary.

8. Gallery walk Fold up the equation Post on wall Rotate with list of equations, trying to decide which is which. With your team, complete your report by detailing your findings from your parabola investigation using the new vocabulary. Which points do you think are important to know? Be sure they are carefully labeled on your graph. What information does the equation give you about the graph? The table? Include any insights you and your teammates find. a. y = x 2 − 2x − 8b. y = −x 2 + 4 c. y = x 2 − 4x + 5d. y = x 2 − 2x + 1 e. y = x 2 − 6x + 5 f. y = −x 2 + 3x + 4 g. y = −x 2 + 2x − 1h. y = x 2 + 5x + 1 i. y = x 2 − 2x – 15j. y = –x 2 + 4x – 5