Copyright 2006 Pearson Education Inc Publishing as Pearson
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8 - 1
8 8. 1 8. 2 8. 3 8. 4 8. 5 8. 6 8. 7 8. 8 8. 9 Quadratic Functions and Equations Quadratic Equations The Quadratic Formula Applications Involving Quadratic Equations Studying Solutions of Quadratic Equations Reducible to Quadratic Functions and Their Graphs More About Graphing Quadratic Functions Problem Solving and Quadratic Functions Polynomial and Rational Inequalities Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
8. 3 Applications Involving Quadratic Equations n Solving Problems n Solving Formulas Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
Solving Problems As we found in Section 6. 5, some problems translate to rational equations. The solution of such rational equations can involve quadratic equations. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8 - 4
Example Cade traveled 48 miles at a certain speed. If he had gone 4 mph faster, the trip would have taken 1 hr less. Find Cade’s average speed. Solution 1. Familiarize. As in Section 6. 5, we can create a table. Let r represent the rate, in miles per hour, and t the time, in hours for Cade’s trip. Distance Speed Time 48 r t 48 r+4 t– 1 Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8 - 5
2. Translate. From the table we obtain and 3. Carry out. A system of equations has been formed. We substitute for r from the first equation into the second and solve the resulting equation: Multiplying by the LCD Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8 - 6
Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8 - 7
4. Check. Note that we solved for t, not r as required. Since negative time has no meaning here, we disregard the – 3 and use 4 to find r: 12 mph. To see if 12 mph checks, we increase the speed 4 mph to 16 and see how long the trip would have taken at that speed: This is 1 hr less than the trip actually took, so the answer checks. 5. State. Cade traveled at 12 mph. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8 - 8
Solving Formulas Recall that to solve a formula for a certain letter, we use the principles for solving equations to get that letter alone on one side. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8 - 9
Example Solve Solution Multiplying both sides by 2 Writing standard form Using the quadratic formula Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8 - 10
To Solve a Formula for a Letter – Say, b 1. Clear fractions and use the principle of powers, as needed. Perform these steps until radicals containing b are gone and b is not in any denominator. 2. Combine all like terms. 3. If the only power of b is b 1, the equation can be solved as in Sections 1. 5 and 6. 8. 4. If b 2 appears but b does not, solve for b 2 and use the principle of square roots to solve for b. 5. If there are terms containing both b and b 2, put the equation in standard form and use the quadratic formula. Copyright © 2006 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 8 - 11
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