10.5 Quadratic Functions and Their Graphs What are your objectives for Section 10.5? How can you accomplish each objective? 1 Graph a Quadratic Function by Shifting the Graph of f(x) x2 • Be able to write the defi nition of a quadratic function in your own words. • Be familiar with the graph of f (x) x2. • Know the defi nition of a parabola and a vertex. • Be able to write the properties of Vertical Shifts and Horizontal Shifts in your own words, with examples. • Understand the property of Refl ection about the x-axis and how that occurs. • Complete the given examples on your own. • Complete You Trys 1–3. 2 Graph f(x) a(x h)2 k Using Characteristics of a Parabola • Follow the procedure for Graphing a Quadratic Function of the Form f (x) a (x h )2 k. • Review procedures for fi nding intercepts. • Follow the procedure for Graphing Parabolas from the Form f (x) ax2 bx c. • Complete the given example on your own. • Complete You Try 4. 3 Graph f(x) ax2 bx c by Completing the Square • Follow the procedure for Rewriting f (x) ax2 bx c in the Form f (x) a(x h)2 k by Completing the Square. • Complete the given example on your own. • Complete You Try 5. 4 Graph f(x) ax2 bx c Using a b 2a , f a b 2b bb • Learn the Vertex Formula. • Complete the given example on your own. • Complete You Try 6. Read the explanations, follow the examples, take notes, and complete the You Trys. 1 Graph a Quadratic Function by Shifting the Graph of f(x) x2 We were introduced to quadratic functions in Chapter 7, and in this chapter we have learned different methods for solving quadratic equations. In this section, we will learn how to graph quadratic functions. Let’s begin with the defi nition of a quadratic function. Definition A quadratic function is a function that can be written in the form f (x) ax2 bx c where a, b, and c are real numbers and a 0. An example is f (x) x2 6x 10. The domain of a quadratic function is (q, q). www.mhhe.com/messersmith SECTION 10.5 Quadratic Functions and Their Graphs 653
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