10.2 Exercises Do the exercises, and check your work. *Additional answers can be found in the Answers to Exercises appendix. Objective 1: Complete the Square for an Expression of the Form x2 bx 1) What is a perfect square trinomial? Give an example. 2) In x2 9x 14, what is the a) quadratic term? x2 b) linear term? 9x c) constant? 14 Complete the square for each expression to obtain a perfect square trinomial. Then, factor. Fill It In Fill in the blanks with either the missing mathematical step or reason for the given step. 3) y2 18y 1 2 1182 9 Find half of the coeffi cient of y. 92 81 Square the result. y2 18y 81 Add the constant to the expression. The perfect square trinomial is y2 18y 81 . The factored form of the trinomial is (y 9)2 . 4) c2 5c 1 2 (5) 5 2 . a 5 2 b 2 25 4 Find half of the coeffi cient of c . c2 5c 25 4 . 25 4 The perfect square trinomial is c2 5c . The factored form of the trinomial is ac . 5 2 b 2 Square the result Add the constant to the expression 16) Can x3 12x 20 0 be solved by completing the square? Give a reason for your answer. No, because the equation is not quadratic. Solve by completing the square. 17) x2 6x 8 0 18) a2 10a 24 0 19) z2 14z 45 0 20) t2 12t 45 0 21) p2 8p 20 0 22) c2 2c 37 0 23) y2 11 4y 24) k2 1 8k 25) x2 10x 3 26) 4b b2 14 27) 2a 22 a2 {4, 2} {12, 2} {5, 9} {3, 15} {2 115, 2 115} {4 117, 4 117} {5 217, 5 217} {2 312, 2 312} 28) w2 39 6w 29) m2 3m 40 0 30) h2 7h 6 0 {1, 6} {8, 5} 31) c2 56 c {7, 8} 32) p2 5p 4 {4, 1} 33) h2 9h 12 34) q2 3 q 35) b2 5b 27 6 36) g2 3g 11 4 37) Can you complete the square on 2x2 16x as it is given? Why or why not? No, because the coeffi cient of x2 is not 1. 38) What is the fi rst thing you should do if you want to solve 3n2 9n 12 by completing the square? Divide both sides of equation by 3. Solve by completing the square. 39) 4r2 32r 55 0 40) 4t2 16t 7 0 1 e 2 41) 3x2 39 30x 42) 5p2 30p 10 43) 7k2 84 49k {3, 4} 44) 10m 2m2 12 {2, 3} 45) 54y 6y2 72 46) 8w2 8w 32 47) 16z2 3 16z 48) 5 16c 16c2 49) 3g2 15g 37 0 50) 7t2 21t 40 0 51) v2 2v 35 0 52) k2 12k 32 0 53) (a 4)(a 10) 17 54) ( y 5)( y 3) 5 55) n 2 3n2 56) 15 m 2m2 57) (5p 2)( p 4) 1 58) (3c 4)(c 2) 3 Solve each problem by writing an equation and completing the square. 59) The length of a rectangular portfolio is 7 in. more than its width. Find the dimensions of the portfolio if it has an area of 170 in2. , 7 2 f {5 213, 5 213} {3 111, 3 111} e 1 4 , 3 4 f e 5 4 , 1 4 f {7, 5} {4, 8} {3 412, 3 412} {1 121, 1 121} e 2 3 , 1 f e3, 5 2 f width 10 in., length 17 in. 5) a2 12a 6) b2 8b 7) k2 10k 8) p2 4p 9) g2 24g 10) z2 26z 11) h2 9h 12) m2 3m 13) x2 x 14) y2 7y Objective 2: Solve an Equation of the Form ax2 bx c 0 by Completing the Square 15) What are the steps used to solve a quadratic equation by completing the square? Answers may vary. www.mhhe.com/messersmith SECTION 10.2 Solving Quadratic Equations by Completing the Square 619
messersmith_power_introductory_algebra_1e_ch4_7_10
To see the actual publication please follow the link above