Answers to Algebra 2 Unit 3 Practice

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1 Answers o Algebra 2 Uni 3 Pracice Lesson a. 0, w, 40; (0, 40); {w w, 0, w, 40} 9. a. 40,000 V Volume c. (27, 37,926) d. 27 unis 2 a. h, r V pr 2 (30 2 2r) c. in. d. 3, in Widh 3. In real-life siuaions, he widh mus be greaer han zero and he volume mus be greaer han zero. 4. C. Sample eplanaion: The formula for volume of a prism or a clinder is he area of he base, which is a second-degree funcion, imes he heigh. Lesson Yes; f () ; degree 3; leading coefficien is D 8. a. The leading coefficien is negaive. As 2, and as, 2. c. -inercep: (2, 0), -inercep: (0, 4) d. relaive min: (0, 4), relaive ma: (1, ) 60 w 21 -inerceps: (20., 0), (0.61, 0), and (.94, 0); -inercep: (0, 1) c. relaive maimum: (0, 1), relaive minimum: (4, 21). Check suden s graph. The minimum number of imes a cubic hird-degree funcion can cross he -ais is one. The maimum number of imes a cubic hird-degree funcion can cross he -ais is hree. Lesson a. even odd 12. The funcion is odd because i is smmeric abou he origin. 13. Sample answer: f () ; he funcion has an even degree (4) bu no all of he eponens are even. The hird erm, 3, has an odd eponen, Odd; an odd funcion mus be an odd-degree polnomial. The end behavior of he graph of an odd funcion decreases on he lef side of he graph and increases endlessl on he righ side of he graph. 1. C 201 College Board. All righs reserved. A1

2 Lesson a. 226 cakes Hannah s Cakes sold 20 more cakes in Januar. 17. a Mari eperiences a loss in Januar. The revenue for he bags seadil increases in December as does he cos o run he business. However, Mari does no eperience a loss unil he business ccle begins again in Januar of he ne ear. c. The break-even poin occurs in he beginning of Februar wih revenue of abou $8000. d. P() P() 18. B 19. a. The relaive maimum for is in Februar, while he relaive maimums for P() and for are in March. The relaive minimum for all hree funcions is in Augus. c. The value of is equal o he sum of and P() for ever value of. d. Subrac he value of P() from he value of o find he value of, since represens he oal revenue from boh cakes and pasries. e. 0; (2, 0) P() f. mid Jul, $11,33; he relaive maimum g. The profi is negaive in Januar when he cos is greaer han he revenue. 20. Answers will var bu should include reducing epenses o increase profi. Check sudens responses. The domain is from Januar hrough December, 0 # # 12. Lesson a c d e a c d D 201 College Board. All righs reserved. A2

3 24. a polnomial. a. V() (12 2 2)(16 2 2) Lesson a c d. 27. a B c d a. Sample answer: I would use long division since one facor is in he form of 1 k Sep 1: Se up he division problem using onl coefficiens of he dividend and onl he consan for he divisor. Include zero coefficiens for an missing erms. Sep 2: Bring down he leading coefficien. Sep 3: Mulipl he leading coefficien b he divisor, wrie he produc under he second coefficien, and add. Sep 4: Repea his process unil here are no more coefficiens. Sep : The numbers in he boom row become he coefficiens of he quoien. The number in he las column is he remainder. Wrie i over he divisor. Lesson a c. 1,04 d. 18, B 34. (a 4 1 4a 3 b 1 6a 2 b 2 1 4ab 3 1 b 4 ) 3. The sum of he eponens of he variables in each erm plus 1 equals he number of erms. There are 1 1 or 6 erms. Lesson a c. 272,160 d. 7, a ,369, c. 27,000,000 3 d. 94,42, ( 2 3) B Lesson a. ( 2 3)( 2 4) (3 2 )( 1 2) c. (3 2 1 )( 2 1)( 1 1) d. ( 1 9)( 2 4) 42. a. ( 2 3)(2 2 1 ) ( 3 1 2)(3 2 1) c. ( 1 )( 2 3)( 1 3) d. ( 2 )( 2 2 3) 43. a. ( 1 )( ) ( 2 2)( ) c. (2 1 6)( ) d. (4 2 3)( ) 44. a. ( )( ) ( 2 1 3)( 2 1 3) 4. D c. ( 3 2 )( 3 2 ) d. (2 2 9)(2 1 9) 201 College Board. All righs reserved. A3

4 Lesson a. 0, 62i; 3 zeros 63, 63i; 4 zeros c. 0 (double), 4 (double); 4 zeros d. 1, ; 3 zeros 3. a a polnomial f () of degree n $ 0 has eacl n linear facors, couning facors used more han once. 48. a C c d a c d Lesson a. I 2. D V c. III d. II e. IV inerceps: (27.6, 0), (0, 0), (0.02, 0), and (6.8, 0); -inercep: (0, 0); relaive minimums: (.39, 2771) and (4.63, 08); relaive maimum: (0.01, 0.00) inercep: (219.13, 0); -inercep: (0, 248); relaive minimum: (212.67, 64); relaive maimum: (0, 248) 201 College Board. All righs reserved. A4

5 4. 60 c. p(2) d. eacl a. Since here are wo sign changes in h() and one sign change in h(2), here are wo or zero real posiive roos and one negaive real roo Since here are hree sign changes in j() and one sign change in j(2), here are hree or zero real posiive roos and one negaive real roo. 9. a. zeros: (22, 0), (1, 0), and (3, 0) -inercep: c. relaive maimum: (21, 8) relaive minimum: (2, 24). a d C -inerceps: (22.026, 0), (0.6, 0), (1.28, 0) and (3.64, 0); -inercep: (0, 1) c. relaive erema: (21.27, 13.02), (2.822, 16.6), and (0.698, 22.76) Lesson a. 61, 6, 6 1 3, , 62, 63, 6 1 2, 63 2, a. 4 4, 2, or 0 Lesson A; he facored form of h() is ( 2 2)( 2 4), so he zeros are 2 and # 22 and 1 # # p(); sample eplanaion: If ou skech each funcion, ou will find ha he range of m() is [0, ) while he range of p() is [2, ), so p() has he greaer range. 64. a.,, 1 and. 8 # 22 and 3 # # 4 6. B 201 College Board. All righs reserved. A