x 2 20x x 10 0 x 10 2x 2 5x 12 2 x x x x Lesson 6.1 Activity (p. 323) 1. 7; 2. a. b. c. d.

Transcription

1 CHAPTER Think & Discuss (p. ). about seconds Speed (ft/sec) Shuttle Speed After Launch Time (sec). A quadratic function would be a good model because the data lies on a curve... ± ± or Skill Review (p. ) Algebra Chapter Worked-out Solution Ke.. ± ± or Lesson. Activit (p. ). ;. a. b. c. d.. m n. a. b. c. d... Guided Practice (p. ) m n. a. product of powers b. power of a power c. power of a product. a. The bases were multiplied; b. The eponents were divided when the should have been subtracted; c. The eponents were mulitplied when the should have been added;. ; product of powers. ; power of a power and product of powers. ; power of a power. ; negative eponent, power of power, and product of powers. ; negative eponent and power of a quotient. ; negative eponent quotient of power. ; product of powers. negative eponent, power of a power, and product of z ; powers. negative eponent and power of a power ;. ; power of a quotient, negative eponent, and power of a product. ; quotient of powers. ; negative eponent, power of a product, quotient of powers, and product of powers Copright McDougal Littell Inc.

2 . Practice and Applications (pp. )...., ,...,...., A sun s volume:. km Earth s volume:. km. A. V Ratio is about,,. Yes, the results match.. V National debt population. France German Ireland Luembourg The Netherlands Sweden.. cm. cm. cm.. km. km da. das.. birds species. species. a.; b. $. $... $. $.. $. $.. $. $. $.. $.... birds $.. $. $.. $ State Total Area Amount of Park space/ (acres) park space Total area Alaska... California... Connecticut... Kansas... Ohio... Pennslvania... c. A good answer should include the percent of area in the state that is now park land, it should also include comparisons with the percents in other states.. a a m a m a m. a m a n a m n a m n am a n Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

3 . Mied Review (p. ) ± ±... i. i. i ± ±. i i. i. i i i Lesson... Activit (p. ). a. b... c. f as f as f as f as d... ±. ±. ± e. f as f as f. f as f as.. ± ± f as f as f as f as CONTINUED Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

4 . CONTINUED. Practice and Applications (pp. ) g. h.. es; f ; ; linear;. If the leading coefficient is positive, the values of the function approach ; if the leading coefficient is negative, the values of the function approach.. When the function s degree is odd, the ends will go in opposite directions. When the function s degree is even, the ends will go in the same direction.. Guided Practice (p. ).,, cubic,.. horizontal line.. no. no. es; es;. f as and f as. f as and f as. f as and f as. f as and f as. f as and f as. f as and f as. f as f as Revenue (millions of dollars) Total Revenue from Home Video Rentals R Years since f as f as t es; f ; ; quartic; es; f ; ; linear; es; f ; ; quadratic; no es; f ; ; constant; es; f ; ; quadratic; no es; f ; ; quartic; no es; f ; ; cubic; no f f f f f f f f. f. f Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

5 Function as as f f f f f f f f f f f f Function as as f f f f f f f f f f f f. f as and f as. f as and f as. f as and f as. f as and f as. f as and f as. f as and f as. f as and f as. f as and f as. f as and f as. f as and f as. f. f. f. f. f. f. f. f. C. D. B. A. f as and f as. f as and f as Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

6 .... f f f f. Sample answer: An polnomial function of odd degree that has a positive leading coefficient will work; f. S.. S. about. million ft. R.... R. about $.. f as and f as ; less; the graph will go down over time..t.t.t.t. Graduates (thousands) U.S. Nursing School Graduates Years since Copright McDougal Littell Inc.... f t f f. f as and f as ; more; the graph will go up over time. about $,,. a. L... L. H... H. Normal range would be. in. to. in. b. f as and f as ; more; the graph will go up over time. P.t.t. Amount of prize (thousands of dollars) c. Woman s U.S. Open Tennis Tournament Prize P t Years since Height (inches) H, L Heifer Minimum/Maimum Normal Height H L Age (months) d. Sample answer: The calf is probabl around months old. I got this b using the graph in part c. I found the height and looked down to find how old the calf was. f g ; Eventuall the combined values of the terms after the leading term will be negligible compared to the value of the leading terms.. Mied Review (p. ) Algebra Chapter Worked-out Solution Ke t f g

7 ... V. ±i. ±i. ±i. ±i. ±i.. ±i. ±i. Developing Concepts Activit. (p. ).,.,.,.,.,.,.,, Lesson.. Guided Practice (p. ). like terms. The negative sign was not distributed over all of the second polnomial ± i ±i. Practice and Applications (pp. ) Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

8 Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

9 V. V C.t.t t t T.t.t t t V.t.t t t.. about,, total vehicles P S Y P.t.t t t, S.t.t.t t Y.t.t.t t,.... about million people P.s.s..s.s..... about. horsepower P D W.t.t t t t.t.t.t.t.t t t t.t.t.t.t t W.t.t.t.t.t t W....., about,, degrees R N P R.t.t.t.t..t.t.t R.t.t.t.t.t.t.t R.t.t.t.t t R.... R, about $, million Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

10 ... C A. a. b. Multipl: Pairs of middle terms will cancel out.. Mied Review (p. ).... I r r r. r r r r r, r, r, r m r r r r r, r, r, r, T M,,r,r,r n n n n... n n n n... ± r r or a b c a b c a b c.... or or or a b c a b c a b c Quiz (p. ) a b c a b c a b c f. f.. a b c a b c a b c Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

11 . f. f. a b a a a b b b a b a b a b a b a ab b. Guided Practice (p. ) f. mi.. hours. mi hr. hr. hr da. da das Lesson. Activit (p. ). Sample answer: The cube a is missing a small part. The part is the cube b. But the total volume can be broken into three parts. B adding the three parts, we get the same volume as we would have if we had taken the total volume of the cube a and subtracted the cube b.. Solid I a a a b Solid II b b a b Solid III a b a b. f. Sample answer:. a. grouping b. difference of cubes c. factoring polnomial. You can t divide b, which contains a variable. Zero is also a solution.. a. b. Sample answer: The graph of does not intersect the -ais, so is not factorable or ± ± or Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

12 ±... ± t t t t t t t The ear was R t t t t t t. Practice and Application (pp. ) C. D. F. A. E. B Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

13 , ±,,.,, ± (...., ±, ±, ±,...,, ±, none; left side is alwas positive ±. none; left side will alwas be a positive number. Sample answer should include:. For two terms, finding a common factor and using the sum/difference of cubes.. For terms, look for a quadratic pattern.. For or more terms, grouping and looking for a common factor.... in.. in.. in.. width: ft length: ft height: ft. ft ft ft., Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

14 ..... ft ft ft. in. b. in. b. in. C D. Sample answer: If we think of the total volume equal to the prisms: a a b, ab a b, and b a b Then a a b a b b a b a b a ab b a b... Mied Review (p. ).... ft ft ft...., ±. D.. Math and Histor (p. ). f... f T s p f Lesson. f. Activit (p. ). ; ; ;... Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

15 . The are equal; the match the coefficients of the quotient.. Guided Practice (p. ). For an number k, the remainder obtained when a polnomial f is divided b k is the value of f when k.. Sample answer:. ; ;.... ) ) ) ), f f,, f,, ) and. about. million radios. Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

16 . Practice and Applications (pp. -) ) ) ) ) ) ) ) ) ) ) ) ) Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

17 f f f f f f,, f f f,, f Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

18 ......,, f, ± f, ± f, ± i,, f f f f f ± i,... ) ) ) f f ) at,,,,,,, Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

19 . at,,. ; multiplied the quotient and remainder b the denominator and added...,,,,, or. about. million cameras..... ) C.... C... C.... C. about million cars... C E ) ) CONTINUED..,.,,.. ).. about $.....,, ) Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

20 . CONTINUED The remainders are all the same, but the coefficients are,, and times larger with snthetic division.. Mied Review (p.)..... ) > > ± ± > > > ± ± ± > ± or es es ± es no Copright McDougal Littell Inc ± ± < < < < es es no < es ± ± ± ±. ±. ±i or..... c v Lesson.. Guided Practice (p. ). constant term, leading coefficient. a. es; coefficients are all integers b. no; coefficients are not all integers c. no; coefficients are not all integers. Make a graph. ±, ±, ±, ±, ±, ±, ±, ±... ±, ±, ±, ±, ±, ±, ±, ±, ±, ±, ±, ± ± ±, ±, ±,, ±, ±, ±, ±, ±, ±, ±, ± ±, ±, ±, ±, ±, ±.. ± i c c f,, ± ± i f,, c v c c c c. ± ± i Algebra Chapter Worked-out Solution Ke

21 ..... f,, f,, f,, f,, in. b in. b in.. Practice and Applications (pp. ). ±, ±, ±, ±, ±, ±, ±, ±. ±, ±. ±, ±, ±, ±, ±, ±. ±, ±, ±, ±, ±, ±, ±, ±, ±, ±, ±, ± ±, ±, ±, ±... ±, ±, ±, ±, ± ±, ±, ±, ±, ±, ±, ±, ±, ±, ±, ±, ±, ± ±, ±, ±, ±, ±, ±, ±, ±. ±, ±, ±, ±, ±, ± none. none.,, f,, f, f f, f f Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

22 .... ±, ± f ±,.... f, ±,,,,, f f f. f,, f,. f,, f ). f,,,,, Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

23 ..... f, f,, f,,,,, , ±,, f f,, f,, f,, f,,, ± ± f f Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

24 ..... f, f,, f,, f,, t t t t t t t t t Copright McDougal Littell Inc.. ft. f in. b in. b in. in. radius, in. height. ft deep, ft wide, ft long. ft b ft b ft Algebra Chapter Worked-out Solution Ke

25 . C. A.,, ; B., ; A. a. ; C. no, no; If a cubic polnomial had or more distinct real zeros, then there would be or more binomials of the form a that divide the polnomial to give a zero remainder. This would impl that the plonomial has degree or greater. However, this is impossible since the polnomial is a cubic polnomial. So a cubic polnomial has at most real zeros. As and, the values of a cubic polnomial approach and, respectivel, or else and. At some value of, therefore, the graph is below the -ais, and at some other values of, the graph is above the -ais. This means that the graph crosses the -ais somewhere between these two values, and the -coordinate of the point where the graph crosses the -ais is a zero.. Mied Review (p. ) a a a a a a a a..... a a a a a a.. or width of mat: in. overall: in. b in. Quiz (p. ) a a a a a ±,,,, ).. a a a a a a.., Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

26 ) ) ) ) f, ± f f,,.. ft ft. ft Lesson. Activit (p. ). a. b. ; ± ; ; rational ; irrational c. ± i, ; ± i ; is rational, are imaginar Sample answer: If f has a degree n >, then f has n solutions.... f,,.., ;. is a solution twice. Guided Practice (p. ). Sample answer: If f is a polnomial of positive degree, then f has at least one root in the set of comple numbers.. Sample answer: The eistence of an imaginar zero would impl that there are two distinct imaginar zeros which is not consistent with the fact that f is degree.. Sample answer: real zeros; no imaginar zeros; the eistence of an imaginar zero would impl the eistence of two distinct imaginar zeros, which would not be consistent with the fact that f has degree. The real number is a repeated zero. Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

27 f.,, f ±, ±i f,, f,, ±i,, f,, i, i f i i, i, i f i i i i,,,, f,, i, i f i i i i i.. Practice and Applications (pp. ). f f es. f f no. f f no. f f es. f f i i i i es. f f i i i i es. f. i, i, i, i f., t t t t, t t t t t, t,,, f,,, Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

28 f. f,, f,, f,,, f,, ±i f, ±i f, ±i f,, ±i f ±i, f,, ±i f,, ±i f,,, ±,.,,, f,, f,, f,, f,, f, i, i f, i, i f i i,, i, i f i, i, i, i f i, i, i, i f i i i i i i i i Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

29 ,, i, i. f i i f,,, i, i f f.,.,. f.,.,. f. f.,. f.,. f.,. f.,. f.,.,.,. E.t.t.t..t.t.t.t.t.t. t. D.t.t t,.t.t t.t.t t t. i i i S.t.t t t t.t.t t t.t.t t t t t.,. late, t. late. a. g, g, g b. g g g c.., %, Sample answer: I graphed and. and found the intersections. a... S.t.t.t.t.t.t.t.t.t t. P.t.t.t.t.t.t t Zeros Sum of zeros Product of zeros,,,,, ±i,,, ± b. Sample answer: If f is a polnomial of degree n, where n >, then the sum of the roots is the opposite of the coefficient of the n term. c. Sample answer: If f is a polnomial of degree n, where n >, then the product of the zeros is the constant term if n is even and the opposite of the constant term if n is odd. a bi a bi a a bi bi a; Since a is real, a must be real. a bi a bi a abi abi bi a b ; Since a and b are real, a b is real.. Mied Review (p. ).. (, ) (, ) (, ) (, ) (, ) (, ) Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

30 .... (, ) (, ) (, ) f (.,.) (, ) (, ). f. f.. f Developing Concepts Activit. (p. )..,., ,.,..,.,.,..,.,.,...,.,...,.,...,.,.; es Lesson.. f. -intercepts:.,. local ma: local min:.,.,,.,.. -intercepts:.,,. local ma: local min:.,..,.. -intercepts:.,,. local ma: local min:,.,.. -intercepts:,,. local ma: local min:.,.,.,.,,.,.. a. < < ; the flaps can t be more than in. b. in. c. in.. f. Guided Practice (p. ). The -coordinate of a point of the graph that is higher than all nearb points.. a. b. c.,.. f. f. f Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

31 . f. f. f. f.... f f f f,,,. local ma: local min: real zeros: degree:. local ma: local min:,,,,. local ma: local min: real zeros: degree:,,,, real zeros: degree:. local ma: local min: real zeros:,,,,,,.,, degree:. local ma: local min:,,,, real zeros: degree:. local ma: local min: real zeros:,,,,, degree:. f. f -intercepts:.,.,. local ma:, local min:, -intercepts:, local ma:, local min:, Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

32 . f. S t t t t t t.t... -intercepts:.,,. local ma:,,, local min:, f -intercepts:.,,. local ma:.,,.,. local min:.,.,., f -intercepts:,,,, local ma:.,.,.,. local min:.,.,.,. f.. at about. seconds The points are the average of oranges in pounds eaten in a given ear since.. about ft. Speed (m/sec) Speed of Swimmer Oranges (pounds) Price inde s r ft.. Seconds f.... r rl rl r l r r l ft P..... P t Years since. V r r r V r r V r r Years since -intercepts:.,.,., local ma:.,. local min:.,.,.,. reaches a local min at.,. ; the producer price inde declined from to a low of about. around September, after which it began to increase.. A polnomial with turning points must be of degree four or higher.. A. B Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

33 . f f. degrees:,, ;,, ; number of times differences were calculated before arriving at a row of constant, nonzero differences:,, ;,, ; the degree equals the number of differences calculated.. ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() f. Guided Practice (p. ). Mied Review (p. ) es;. es;. no. es;. a. a.. Lesson. Developing Concepts Activit (p. ) Drawing Conclusions. a. a a c a c a b c b. c. a a in. da ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ(). a a a c a c a b c. the difference between f n and f n, etc.; the difference of adjacent first-order differences.. because the points will not lie eactl on the line generated b the model a a a f ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() rd degree Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

34 . degree. f. f. d n n. Practice and Applications (pp. ) Practice and Applications (pp. ).. nd f a a a f f a a a f f a a a f f a a a f f a a a f f a a a f f a a a f f a a a f Copright McDougal Littell Inc.. f a. ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() a a f. ƒ() ƒ() ƒ() ƒ() ƒ() ƒ(). ƒ() ƒ() ƒ() ƒ() ƒ() ƒ(). ƒ() ƒ() ƒ() ƒ() ƒ() ƒ(). ƒ() ƒ() ƒ() ƒ() ƒ() ƒ(). ƒ() ƒ() ƒ() ƒ() ƒ() ƒ(). ƒ() ƒ() ƒ() ƒ() ƒ() ƒ(). ƒ() ƒ() ƒ() ƒ() ƒ() ƒ(). ƒ() ƒ() ƒ() ƒ() ƒ() ƒ(). f. f. f. f f.. f f f f f f f.. ƒ() ƒ() ƒ() ƒ() ƒ() ƒ( ƒ() ƒ() ƒ() ƒ() ƒ() ƒ(.. f n n n n f t.t.t.t f... f. about, Girl Scouts Algebra Chapter Worked-out Solution Ke

35 ... Mied Review (p. ) about $,.t.t t. t. t t.t.t t t about seconds. a. Dog-walking:.. Lawn-care:.. b. Sample answer: Solve for in both equations when. Dog walking profits in December equal $ while lawn care profits are $.. a. f... f f f f f ± ±.. ± a b c d a a a a b b b c c d a a a a b b b c c d a a a a b b b c c d a a a a b b b c c d a a a a b b b c c d b. f. ± ±,. ± ± a a a b b c a a a b b c a a a b b c a a a b b c a a a b b c.. ± ± ± i ± i a a b a a b a a b a a b. ±, a a a Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

36 .. i i i i ±,. local ma:.,.. local min:.,.. local ma:.,. local min:.,,.,. local ma:.,. ± i local min:.,. ± i. local ma:, local min:.,.... a... a a.... a a Quiz (p. ) f.,.,. f ± i, f,, ±i f,,, i i i i i i.. a a a a a. f. f. N... Chapter Review (pp. ). negative eponent and power of a ; quotient properties a a. ; negative eponent, power of a quotient, quotient of powers, and zero eponent properties. negative eponent, product of ; powers, and quotient of powers properties. negative eponent, quotient of ; powers, and zero eponent properties Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

37 .... f. f. ) f,. f. f,. -intercepts:, local ma:.,. local min:, intercepts:, local ma:, local min:,..,. -intercepts:,. local ma: none local min:,,,. ). ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

38 . Chapter Test (p. ) ). a. a a f as, f as f as, f as ±, ± i ±, ± i f as, f as, ,,,,, ±i ±, ±, ±, ±, ±, ±, ±, ±; f,, ±i, ±, ±, ±, ±; f ±, ±, ±, ±, ±, ±, ±, ±, ± f f f f f i i f..,.,. Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

39 .... -intercepts: ± local ma: local min:,,,, Chapter Standardized Test (pp. ).. f D f f A. f f as A. f t.t.t.t.t, f. C. E., ± A. f. a. D. A f as f as ƒ() ƒ() ƒ() ƒ() ƒ() ƒ() f n n n n... in. mi mi in. ft B. f f,, E. mi. f zeros E a a D. a. f b. c. no; the local ma occurs at about.,. and the local min occurs at about.,., but must be greater than for the side of length to have a positive measure. d. ft b ft b ft. a. b. f n n n n c. f n n n n ; for prism n, the dimensions are n b n b n d. e. f, ƒ(n) (, ) (, ) (, ) (, ) (, ) (, ) n The domain is all positive integers. Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

40 Cumulative Practice, Chapters (pp. ) or or > >... f,, if if > <. < < <. f,, if < if. < <. or. m. m. m. m.... >.... det A z.,, Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

41 . det A.,,. z <.. z. z.. (,, ) z. z (,, ).. ± no inverse; det > > < or >, ±.. ±. ±i ± or ±., ±. i i i i i. i i i Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.

42 .. i i i i i. a. a a a a b c a b c a b c..... f,, f ±, ±i f ±i, a a a a a a. r I r.% Pt ; a a.. negative correlation. after minutes.. Number of loaves b A E X I T t N O W Years since. mi. h. mi h,,,, Copright McDougal Littell Inc. Algebra Chapter Worked-out Solution Ke

43 Project Chapters (pp. ). es; The resulting matri is a magic square with a magic constant of.. es; The result is alwas a magic square. The magic constant in terms of a is a.. Answers ma var.. es; The result is a magic square with a magic constant of.. The transpose is also a magic square with a magic constant of.. The diagonal gives us a magic constant of, so the magic square can be completed using trial and error until a match is found.. The sum of the entries are for the magic square and for the magic square.. S n n is a quartic function.. M n n is a cubic function. Etension: S M n a n a n n Algebra Chapter Worked-out Solution Ke Copright McDougal Littell Inc.