Chapter 10: Review Exercises (10.1) Solve using the square root property. 1) w2 81 {9, 9} 2) p2 50 0 {512, 512} 3) 3a2 7 40 4) (z 6)2 20 5) 5 (k 4)2 14 6) 35 (2y 1)2 7 7) a3 {111, 111} {6 215, 6 215} e 1 217 2 , 2 2 14 e12, 4 c 5b 1 217 4 3 f 2 f 8) The power, P (in watts), in an electrical system is given by P V2 R , where V is the voltage, in volts, and R is the resistance, in ohms. Find the voltage if the power is 45 watts and the resistance is 5 ohms. 15 volts (10.2) Complete the square for each expression to obtain a perfect square trinomial. Then, factor. 9) x2 18x 10) n2 20n x2 18x 81; (x 9)2 n2 20n 100; (n 10)2 11) z2 3z 12) y2 y z2 3z 9 4 ; az 3 2 b 2 y2 y 1 4 ; ay 1 2 b 2 Solve by completing the square. 13) d 2 10d 9 0 14) v2 8v 11 0 15) r2 15 4r 16) x(x 14) 24 {12, 2} 17) a2 5a 2 0 18) t2 7 3t 19) 4n2 8n 21 20) 2h 7 2h2 {9, 1} {4 15, 4 15} e 3 2 , 7 2 f e 1 2 115 2 , 1 2 115 2 f (10.3) 21) We can use the quadratic formula to solve ax2 bx c 0 (a 0) for x. Write the quadratic formula. x b 2b2 4ac 22) Correct the error in this simplifi cation: 6 3110 3 6 110 2a Solve using the quadratic formula. 23) x2 7x 12 0 24) 3z2 z 10 0 25) 2r2 3r 6 26) 8n2 3 14n 27) t(t 10) 7 {5 312, 5 312} 28) 1 y(5 4y) 29) 3 8 p2 1 2 p 1 4 {4, 3} e 5 141 0 e2, e 1 4 , 3 2 f 5 3 f 8 , 5 141 8 f e2 110 3 , 2 110 3 f 30) (2w 3)(w 4) 6(w 1) 31) The hypotenuse of a right triangle is 1 inch less than three times the shorter leg. The longer leg is 155 inches long. Find the length of the shorter leg. 3 in. Solve. Give an exact answer, and use a calculator to round the answer to the nearest hundredth. 32) An object is thrown upward from a height of 26 feet. The height h of the object (in feet) t seconds after the object is released is given by h 16t2 22t 26 a) How long does it take the object to reach a height of 6 feet? 2 sec b) How long does it take the object to hit the ground? (Hint: When the object hits the ground, h 0.) 11 1537 16 sec or about 2.14 sec Mixed Exercises Keep in mind the four methods we have learned for solving quadratic equations: factoring, the square root property, completing the square, and the quadratic formula. Solve the equations using one of these methods. 33) d 2 3d 28 0 {4, 7} 34) 2y(y 3) 1 35) (3t 1)(t 1) 3 36) 1 18 p2 7 9 p 8 3 0 {8, 6} 37) (n 9)2 7 12 38) (3a 4)2 15 11 39) 6c3 12c 38c2 , 6 f 40) 4m2 25 0 e 41) k 2 5k2 3k 4 42) w2 6w 4 0 43) h2 4h {0, 4} 44) 0.01x2 9 133 0.09x 0.12 0 e2 5 2 , 5 2 {3 15, 3 15} , 9 133 2 f {9 15, 9 15} e 0, 1 3 (10.4) 45) What do you call the graph of y ax2 bx c (a 0)? 46) Explain how to fi nd the vertex of the graph of y ax2 bx c (a 0). 47) What is the axis of symmetry of a parabola? Sketch the graph of each equation. Identify the vertex. 48) y x2 4 vertex: (0, 4) 49) y (x 2)2 50) y x2 4x 3 51) y x2 2x 2 52) y x2 6x 11 vertex: (3, 2) (10.5) Identify the domain and range of each relation, and determine whether each relation is a function. 53) {(6, 0), (5, 1), (8, 1), (10, 4)} 54) {(2, 4), (2, 4), (3, 9), (3, 16)} 55) CD DVD Blu-ray disc Music Movie PS3 www.mhhe.com/messersmith CHAPTER 10 Review Exercises 657 f parabola vertex: (2, 0) vertex: (2, 1) vertex: (1, 3) domain: {6, 5, 8, 10}; range: {0, 1, 4}; function domain: {2, 2, 3}; range: {4, 9, 16}; not a function domain: {CD, DVD, Blu-ray disc}; range: {Music, Movie, PS3}; not a function *Additional answers can be found in the Answers to Exercises appendix. e 3 2 137 2 , 3 2 137 2 f
messersmith_power_introductory_algebra_1e_ch4_7_10
To see the actual publication please follow the link above