What are your objectives for Section 10.1? How can you accomplish each objective? 3 Use the Distance Formula • Understand the defi nition of the distance formula. • Review the Pythagorean theorem. • Complete the given example on your own. • Complete You Try 4. 4 Complete the Square for an Expression of the • Learn the procedure for Completing the Square for x2 bx. • Review factoring of perfect square trinomials. • Complete the given examples on your own. • Complete You Trys 5 and 6. 5 Solve a Quadratic Equation by Completing • Learn the procedure for Solving a Quadratic Equation by Completing the Square. • Review the square root property. • Complete the given example on your own. • Complete You Try 7. Read the explanations, follow the examples, take notes, and complete the You Trys. We defi ned a quadratic equation in Chapter 7. Let’s restate the defi nition: Definition A quadratic equation can be written in the form ax2 bx c 0, where a, b, and c are real numbers and a 0. Form x2 bx the Square In Section 7.4 we learned how to solve quadratic equations by factoring. For example, we can use the zero product rule to solve x2 3x 40 0. x2 3x 40 0 (x 8)(x 5) 0 Factor. b R x 8 0 or x 5 0 Set each factor equal to zero. x 8 or x 5 Solve. The solution set is {5, 8}. It is not easy to solve all quadratic equations by factoring, however. Therefore, we need to learn other methods. In this chapter, we will discuss three more methods for solving quadratic equations. Let’s begin with the square root property. 1 Solve an Equation of the Form x2 k Look at the equation x2 9. We can solve this equation by factoring, like this: x2 9 x2 9 0 Get all terms on the same side. (x 3)(x 3) 0 Factor. b R x 3 0 or x 3 0 Set each factor equal to zero. x 3 or x 3 Solve. Look at Section 7.4 if you need a detailed review of solving quadratic equations by factoring. www.mhhe.com/messersmith SECTION 10.1 The Square Root Property and Completing the Square 611
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