1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 8-1 Quadratic Functions Chapter 8

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – Solving Quadratic Equations by Completing the Square 8.2 – Solving Quadratic Equations by the Quadratic Formulas 8.3 – Quadratic Equations: Applications and Problem Solving 8.4 – Writing Equations in Quadratic Form 8.5 – Graphing Quadratic Functions 8.6 – Quadratic and Other Inequalities in One Variable Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 8-3 § 8.3 Quadratic Equations: Applications and Problem Solving

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 8-4 Solve Additional Applications Example OppRtunity, a start-up company, projects that its annual profit, p(t), in thousands of dollars, over the first 6 years of operation can be approximated by the function p(t) = 1.2t 2 + 4t – 8, where t is the number of years completed. a.) Estimate the profit (or loss) of the company after the first year. continued

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 8-5 Solve Additional Applications To estimate the profit after 1 year, we evaluate3 the function at 1. continued Thus, at the end of the first year the company projects a loss of $2.8 thousand or a los of $2800.

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 8-6 Solve Additional Applications b.) Estimate the profit (or loss) of the company after 6 years. continued Thus, at the end of the sixth year the company’s projected profit is $59.2 thousand, or a profit of $59,200.

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 8-7 Solve Additional Applications c.) Estimate the time needed for the company to break even. The company will break even when the profit is 0. Thus, to find the break-even point (no profit or loss) we solve the equation continued

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 8-8 Solve Additional Applications We can use the quadratic for to solve this equation. Since time cannot be negative, the break-even time is about 1.4 years.

9 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 8-9 Solve for a Variable in a Formula Example The formula for the area of a circle is. Solve this equation for the radius, r.

10 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 8-10 Solve for a Variable in a Formula Example The diagonal of a box can be calculated by the formula Where L is the length, W is the width, and H is the height of the box. Find the diagonal of a suitcase of length 30 inches, width 15 inches, and height 10 inches.

11 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 8-11 Solve for a Variable in a Formula To find the diagonal, we need to substitute the appropriate values into the formula and solve for the diagonal, d. Thus, the diagonal of the suitcase is 35 inches.