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REVIEW Skills Review Handbook p. 992; TAKS Workbook REVIEW TAKS Preparation p. 146; TAKS Workbook 67. ★ EXTENDED TAKS REASONING RESPONSE A U.S. Postal Service guideline states that for a rectangular package like the one shown, the sum of the length and the girth cannot exceed 108 inches. Suppose that for one such package, the length is 36 inches and the girth is as large as possible. a. What is the girth of the package? b. Write an expression for the package’s width w in terms of h. Write an equation giving the package’s volume V in terms of h. c. What height and width maximize the volume of the package? What is the maximum volume? Explain how you found it. 68. CHALLENGE Recall from geometry the theorem about the products of the lengths of segments of two chords that intersect in the interior of a circle. Use this theorem to find the value of x in the diagram. MIXED REVIEW FOR TAKS 69. TAKS PRACTICE A pizza is divided into 12 equal slices as shown. The diameter of the pizza is 16 inches. What is the approximate area of one slice of pizza? TAKS Obj. 8 A 15.47 in. 2 C 21.21 in. 2 QUIZ for Lessons 4.1–4.4 B 16.76 in. 2 D 67.02 in. 2 Graph the function. Label the vertex and axis of symmetry. (p. 236) 3x 1 2 5x 2 4 1. y 5 x 2 2 6x 1 14 2. y 5 2x 2 1 8x 1 15 3. f(x) 523x 2 1 6x 2 5 Write the quadratic function in standard form. (p. 245) 4. y 5 (x 2 4)(x 2 8) 5. g(x) 522(x 1 3)(x 2 7) 6. y 5 5(x 1 6) 2 2 2 Solve the equation. 7. x 2 1 9x 1 20 5 0 (p. 252) 8. n 2 2 11n 1 24 5 0 (p. 252) 9. z 2 2 3z 2 40 5 0 (p. 252) 10. 5s 2 2 14s 2 3 5 0 (p. 259) 11. 7a 2 2 30a 1 8 5 0 (p. 259) 12. 4x 2 1 20x 1 25 5 0 (p. 259) x 1 1 70. TAKS PRACTICE While shopping at Store A, Sam finds a television on sale for $210. His friend tells him that the same television at Store B is on sale for $161. About what percent of the cost of the television at Store A does Sam save by buying the television at Store B? TAKS Obj. 9 F 20% G 23% H 30% J 77% 13. DVD PLAYERS A store sells about 50 of a new model of DVD player per month at a price of $140 each. For each $10 decrease in price, about 5 more DVD players per month are sold. How much should the store charge in order to maximize monthly revenue? What is the maximum monthly revenue? (p. 259) EXTRA PRACTICE for Lesson 4.4, p. 1013 ONLINE QUIZ at classzone.com 2x TAKS PRACTICE at classzone.com �� 265
TEKS 4.5 2A.6.A, 2A.6.B, 2A.8.A, 2A.8.D Key Vocabulary • square root • radical • radicand • rationalizing the denominator • conjugates Before You solved quadratic equations by factoring. Now You will solve quadratic equations by finding square roots. Why? So you can solve problems about astronomy, as in Ex. 39. USE A CALCULATOR You can use a calculator to approximate Ï } s when s is not a perfect square. For example, Ï } 80 ø 8.944. Solve Quadratic Equations by Finding Square Roots A number r is a square root of a number s if r 2 5 s. A positive number s has two square roots, written as Ï } s and 2Ï } s. For example, because 3 2 5 9 and (23) 2 5 9, the two square roots of 9 are Ï } 9 5 3 and 2Ï } 9 523. The positive square root of a number is also called the principal square root. The expression Ï } s is called a radical. The symbol Ï } is a radical sign, and the number s beneath the radical sign is the radicand of the expression. E XAMPLE 1 Use properties of square roots Simplify the expression. 266 Chapter 4 Quadratic Functions and Factoring KEY CONCEPT For Your Notebook Properties of Square Roots (a > 0, b > 0) Product Property Ï } ab 5 Ï } a p Ï } b Example Ï } 18 5 Ï } 9 p Ï } 2 5 3Ï } 2 Quotient Property Î } a }b 5 Ï} a } b a. Ï } 80 5 Ï } 16 p Ï } 5 5 4Ï } 5 b. Ï } 6 p Ï } 21 5 Ï } 126 5 Ï } 9 p Ï } 14 5 3Ï } 14 c. Î } 4 } 5 81 Ï} 4 } Ï 81 5 2 } 9 Ï } Example Î } 2 } 5 25 Ï} 2 } Ï 25 d. Î } 7 } 5 16 Ï} 7 } Ï 16 Ï} 5 7 } 4 Ï} 5 2 } 5 SIMPLIFYING SQUARE ROOTS You can use the properties above to simplify expressions containing square roots. A square-root expression is simplified if: • no radicand has a perfect-square factor other than 1, and • there is no radical in a denominator ✓ GUIDED PRACTICE for Example 1 Simplify the expression. 1. Ï } 27 2. Ï } 98 3. Ï } 10 p Ï } 15 4. Ï } 8 p Ï } 28 5. Î } 9 } 64 6. Î } 15 } 4 7. Î } 11 } 25 8. Î } 36 } 49
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