1 Find the roots of the quadratic equation i-16y - 57 = 0 using the quadratic formula...4-(i:-:y::--sl7". 1.= -(-Io)! rj'-{--io)p:- A -3 and -19 v,! 'A t1/ij'ltfto '2 W= Y-3 and 19 )(=-1o44 C 3 and -19 :: to._ + '2. '2. D 3 and 19 -- "'L-- v>+ \'1 5 Find the roots of the quadratic equation i + lly - 60 = 0 using the quadratic formula.,\\-tar;\"l.. Ii i.:.\ '" -... _ \1 \ "I.\ l..-,t-uj A -4 and -15 -\\t.-{\2\4,v\b B -4and15 + J - f7;\.a - \ \ - '\ vlo,\ \'S.r and -15 '-D'4 and 15 :.':' \!. \:1 -l\+\q? 1,. = 4- I,I I 2 Find the roots of the quadratic equation 9x 2 + 3x - 4 = 0 using the quadratic formula. '/. :..3:t'\J31.-4(9.1 "O.i A-3 \ and -3-1 -3'!C\..H4 'B" -3 + Vi55 d -3 - Vi55-5!-1\5i'"" 18 an 18 -'L{ C\ ') C -3 + Vi57 and -3 18 - Vi57 18 2..l...r:-::- - -..,).:. "ills3' -3 + v163-3 _ v163 ''IS'='- D 18 and 18 'SInOU\e.i- \rtclve.., b"\'/v\ \\(1{';\ lou,tth-t;l\ "f.1c\\ct\rtt: Z"ii1 3 Find the roots of the quadratic equation l \Oe..WCt.e; y2 + 18y + 56 = 0 using the quadratic formula. i ':.-\lot (If() 'Z._4(l) (5ft,) A -8 and -7 -\D± '\j?a:"2..2a <i\ 4 and -14 - \ <0 1.-'_' + ""r \J too C 8 and 7 - \ )t io - te:t'\o D 4 and 14 ll:t -1..'--;:..; ;z::--- -: -r--'-\ 1.. "i -\4 -lc)-\--\d - -It:! \b -Us 6 Find the roots of the quadratic equation 5x 2-4x - 2 = 0 using the quadratic formula. :/,-:;.- (il'):t'\ {:''l(5170-2 + Vi4-2 - Vi4. - A 10 and 10 it! \(g-t 4D B -2 +5Vi4 and -2-5Vi4 4t.; 'f1 C 2 + Vi4 and 2 - Vi4-1.(5) =lcd 10 10...,- 1)'i:2+ Vi4 a d 2 - Vi4. >"IfI L n 5 / \.- 1.. 1:!ffl ill 1)\.!5' L 1.:'- 7 Find the roots of the quadratic equation y2-4y - 45 = 0 using the quadratic formula. A -15 and 3 B 15 and -3 'i-(-b\ J 1. {-I.\ :.1\(\ Y.4:5/ X -:. 1\lt>+ tsd C -9and5 \ -'\ -:t"-\j \ C\ lc '(D;,9 and -5 l\t \'-\ 'T' 4 Find the roots of the quadratic equation x2 + x - 15 = 0 using the quadratic formula. /-:-\ti)i4('v\ A -1 + v58 and -1 - v58. +_r'",,,",b.,.-- 2 2 -\-. t -\oldl) -1 B + v59 d -1 - v59 \-t:'-<'fi_=\ 2 an 2 -.: C -1 + V60 and -1 - V60. 2 2 )-1 + V61 and -1- V61 2 '2 -:" CA Standards Review LESSON 21 Using the Quadratic Formula to Find Roots 63
,1. 1 ji'. 1 11'1 ' 'l ',1 1What are the x-intercepts of the graph of the equation y = x2 + x - 2? A -2 and -1-2and1 ( C 2 and+-i D 2 and 1 Name'_-L-l- Class :Z5 4 What are the zeros of the function graphed below? r A -8 and-5 B -5 and 0 C' -8 and -2 D -3 and-7 3 What are the solutions of the quadratic equation 3x 2 + 9x - 12 = O? Q-\ -:t' C", "h ",' l\') :::.b A -1and-4 B -land4 -:'\1.-._X -1. 1 and 4. ;,.\ '" "1..7... -X (?'l and-4 3y... t4 \":31<. -"1- (X-l X i4).=to 'A -, :::.0 X it L\=-Q X<:::\ X-L\ 5 What are the zeros of the function graphed below? 01and+-I Bland 0 C 0 and 0 D -1 and 0 66 LESSON 22 Roots, Zeros, and x-intercepts of Quadratic Functions CA Standards Review
1 How many x-intercepts does the quadratic function y = x2 + 4x + 6 have? y 1 'l.-t\dc., 0 t=\ 'f\ a -fin e d\ i. 'bcr \ \II\ \10 n 'r C 2 (4) 1:-'t1.\':[(g)..-tt mfs Name,_---!&.t:---Class:-!!fE== \,(P> - 2.'; -:::. there oxe D Cannot be determined t:.e.xtj 5t>\., l'h4. d() c.**,,", 'Y.--o.:t5. 4 Factor to find the number of x-intercepts of the quadratic function y = x2-12x + 36. A 0 ; (-(pj(-f.l).=-b Jji't 1 -td.,-wy. )(:...tp::o }(-fo,b -\7.:i X""" IA v- c: C 2 -w 1\-11t-'. D Cannot be determined '<>1',\ I \'\ \L. F' \in- 1,...<. 2 The following is a graph of the quadratic. function y = - x2 + 7. How many x-intercepts does it have? 5 Use the quadratic formula to find the number of x-intercepts of the quadratic function y = -6x2 + 5x + 1. b- 40-.G AO 5t-4 (--lg-:(l) VO'\\\'ve...:\t: B,1 S 4 l Q.'f\ w-e"r c: '2 4q mt.(a,tt+hie. D Cannot be determined A Sl 0 If) 2. po\f\+ DV\+he \s AO B 1 2 D Cannot be determined 3 Use the quadratic formula to find the number of x-intercepts of the quadratic function y = -x 2 + x - 1. <00 B 1 C 2,",,,f), u -- f\ O\,G. l\) '2:ll, (a\)( \) \_,fl _';?.,\ 'to D Cannot be determined 6 How many x-intercepts does the quadratic function y = 9x 2 + x + 1 have? ({;;o b1..-t\q.'-' t\l.-(c1'ii) _"", B 1 C 2 \ - fo :::_.E:> 5 # D Cannot be determined.j...> c \U:\ \(SV fj X\!V\-kK:. l\)o rdo1s 7 Faftot to find the number of x-intercepts of 1:::: the quadratic function y = 5x 2-18x - 8. -'2- "l-. -,-- x > 5 A 0 -t.iny. X - '1 1, ;:\t+!;p 2! c: -, I,--\ r' p' e, \ ") D Cannot be determined l, ''""\,, t 0,-,\ (' 'f\ CA\,. o \) ",: _xyve.. d. \\_,or \ fl{\ \ 'f,ctrrrf' \.. CA Standards Review LESSON23 Determining the Number of x-intercepts 69
Name_*'dlll'- 1A firecracker was projected into the air. Its height is plotted versus time on the graph below. Trajectory of a Firecracker Time (seconds) exploded What is a correct conclusion about this graph? A The firecracker was shot from a height of O. B The firecracker returned to the ground before it exploded. r The firecracker reached its maximum height and began to fall before it exploded. D The height at which the firecracker exploded was less than the height from which it was shot. 2 The shape of one portion of a rollercoaster is plotted on the graph below..., -----Class-----, Use the table below for questions 3 and 4. The heights of a model rocket during its flight are shown in the table. Time (s) o Height (m) o 1 60 2 104 3 132 4 144 5 140 6 120 7 84 8 32 3 About how many seconds after the launch did the rocket reach its maximum height? A 2 seconds q)4seconds C 5 seconds D 8 seconds 4 How many seconds do you think passed before the rocket hit ground? A 8 seconds tifyiess than 9 seconds about 10 seconds D more than 10 seconds From the graph, what conclusion can be made about the shape of this portion of the rollercoaster? A The lowest point is 1.5 m off the ground. B The right and left sides reach the same maximum height. C The vertical and horizontal distances are always the same. The maximum height is 10 m. 72 LESSON24 lnterpretlnq Quadratic Relationship CA Standards Review
Name,_----Q, 1 If that car has seatbelts, then that car is safe to drive. That car has seatbelts. Therefore, what must be true? -----Class,------ F'-"'iIF- ::t My socks are dirty. All dirty things need to be washed. Therefore, what must be true? A If they aren't my socks, then they don't need to be washed A That car doesn't have seatbelts. l That car is safe to drive. B My socks aren't dirty. C That car isn't safe to drive. y socks need to be washed. D If that car is safe to drive, then that car has seatbelts. y socks don't need to be washed. 2 Which of the following is an example of the Law of Syllogism? A If my shoe is untied, then I might slip and fall. My shoe is untied. Therefore, I might slip and fall. B If this is a diamond, it is a precious jewel. This is a diamond. Therefore, it is a precious jewel. C If he didn't train properly for the race, then he won't have a good time. He didn't train properly for the race. Therefore, he won't have a good time. ' this If hsis a srawbery,then this is a fruit. If ISa fruit, then It must be good for 5 Which of the following is an example of the Law of Detachment? IA'\If I ride my bike at night, then I must use reflectors. I ride my bike at night. Therefore, I must use reflectors. B If I go to the zoo, then I'll see a lot of animals. If I see a lot of animals, then I'll have a good time. Therefore, if I go to the zoo, then I'll have a good time. C If she gets good grades, then she'll get a scholarship. If she gets a scholarship, then her parents will be happy. Therefore, if she gets good grades, then her parents will be happy. > you. Therefore, if this is a strawberry, then it must be good for you. D If it rains, then it pours. If it pours, then we'll all get wet. Therefore, if it rains, then we'll all get wet. 3 Which of the following is a valid argument? A If she didn't eat dinner, then she must be hungry. She ate dinner. Therefore, she - must not be hungry. If it's good, then it's really good. If it's really good, then it's great. Therefore, if it's good, then it's great. C If the alarm clock goes off, then I'll wake up in time. If I wake up in time, then I won't be late. Therefore, if I wake up on time, then the alarm clock will have gone off. D If I watch too much television, then I'll get lazy. I got lazy.therefore, I watched too much television. CA Standards Review LESSON 2S Logical Arguments 75
1 Which of the following is an example of inductive reasoning? A All good students do their homework. Ryan is a good student. Therefore, Ryan does his homework. e, an has done his homework ever night this school year. Therefore, Ryan will always do his homework. C Ryan's teacher has declared that all students who do not do their homework will not pass the class. Ryan concludes that since he has not done his homework, he will not pass the class. 3 Which of the following is an example of inductive reasoning? ItlAll of Katie's Vall goldfish are gold. Therefore, goldfish are gold. B Since not all goldfish are gold, the next goldfish that Katie buys might not ; begold. C All of Katie's goldfish are gold. Therefore, at least some goldfish are gold. D All of Katie's goldfish are gold. Therefore, none of Katie's goldfish are not gold. D Ryan does his homework. Therefore, Ryan's teacher concludes that at least some of her students do their homework. 4 Which of the following is an example of deductive reasoning? 2 Which of the following is an example of deductive reasoning? A Every basketball player Charel has ever met has been over 6 feet tall, so all basketball players are over 6 feet tall. B Every basketball player Charel has ever met has been over 6 feet tall, so the next basketball player that Charel meets will be over 6 feet tall. )Not every basketball player Charel has - ever met has been over 6 feet tall, so not all basketball players are over 6 feet tall. A The past 10 winners of a particular school's annual spelling bee have been girls, so next year's winner of the spelling bee will be a girl. B The past 10 winners of a particular school's annual spelling bee have been girls, so girls. will always win the spelling bee. The past 10 winners of a particular school's annual spelling bee have been girls, so last year's winner of the spelling bee was a girl. D The past 10 winners of a particular school's annual spelling bee have been girls, so the next 10 winners of the spelling bee will be girls. D Not every basketball player Charel has ever met has been over 6 feet tall, so the next basketball player that Charel meets will not be over 6 feet tall. -d Q) e.g> <i: -a =e =.:::.::: 0 0 C1> c... '" '".::: "".:c ::::> 0.. U.:::0 -..:::- 8 ::::>....::: 0 <::> c... Q) -. "" =0 '-' 78 LESSON 26 Inductive and Deductive Reasoning CA Standards Review i