Chapter 10

messersmith_power_introductory_algebra_1e_ch4_7_10

CHAPTER 10Quadratic Equations OUTLINE Study Strategies: Creating Visuals 10.1 Solving Quadratic Equations Using the Square Root Property 10.2 Solving Quadratic Equations by Completing the Square 10.3 Solving Quadratic Equations Using the Quadratic Formula Putting It All Together 10.4 Graphs of Quadratic Equations 10.5 Introduction to Functions Group Activity emPOWERme: What’s Your Learning Style? Math at Work: Ophthalmologist We have already seen two uses of mathematics in Mark Diamond’s work as an ophthalmologist, and here we have a third. Mark can use a quadratic equation to convert between a prescription for glasses and a prescription for contact lenses. Specifi cally, after having reexamined a patient for contact lens use, Mark can use the following quadratic equation to double-check the prescription for the contact lenses based on the prescription his patient currently has for her glasses: 602 Dc s(Dg)2 Dg where Dg power of the glasses, in diopters s distance of the glasses to the eye, in meters Dc power of the contact lenses, in diopters If the power of a patient’s eyeglasses is 9.00 diopters and the glasses rest 1 cm or 0.01 m from the eye, the power the patient would need in her contact lenses would be Dc 0.01(9)2 9 Dc 0.01(81) 9 Dc 0.81 9 Dc 9.81 diopters An eyeglass power of 9.00 diopters would convert to a contact lens power of 9.81 diopters. Mark realizes that his work is complex. Nonetheless, he wants his patients to understand what is happening with their eyes and how he is treating them. To help explain, he often refers to diagrams of the eye and other visuals that he keeps in his offi ce. These visuals can make ideas that might otherwise be confusing simple and straightforward. In this chapter, we will learn different ways to solve quadratic equations and introduce strategies for creating visuals.


messersmith_power_introductory_algebra_1e_ch4_7_10
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