Name: 1. Find the value of r., (r + 4) 2 = 48 4_ {1 1:. r l f 11i),_ == :r (t~ : t %J3 (t:; KL\J5 ~ ~ v~~f3] ntegrated : Unit 2 Study Guide 2. Find the value of s. (s 2) 2 = 200 ~ :!:[Uost ~~::~~n '!JJori s: ~ &:Ll()J~ 4. Determine the roots of the equation x 2 + Sx 36 = 0. X O 5.!:) (5)14( )(J& ) 2(1') f., :,J...j 2<;;tl4' 2..,c, _,,.!:~ 5:!. t3 ~ 5. Determine the roots of the equation x 2 x 42 = 0.!< :... ( 1)1)<.:1; 't( )('{t) L(1) /( ;_ l±j 1 r1. ~ z... 6. Determine the roots of the equation x 2 Sx 14 = 0. ;(, : ('5).! J{() 'l.._, y(,)(1'4) 2( t) 7. Calculate the roots of the Verify your solution. 3x 2 + 10x + 8 = 0 '. :. (0 ::t [(lo)z.1f(,3){ ~) 2.,(,?,) X:. OiJ 100 _ "i,._ 10:!.Fi (., «> " l o + "'.,. o + 2. 'ir j, " ~ :.,,. T.::: r 3 (p f=t y 0 0 ')) ~ :;, 12 _ 1 b J (p ~") 8. Calculate the roots of the Verift; your solution. 4x 2 + 1 Ox + 6 = 0 X:; 10.:1' J(!o)1. Lf(l/)() x :: 2( (..l) l oj. J 1.:> u4 v_ lo:!. fl E, ~ 9. Calculate the roots of the Verify your solution. 5x 2 + 7x 6 = O, i,~ Y1' l((5~(.) )(7~ 2.c.. 5) Y: :. 1.:t J 4,H1½! ;1~ lo { o x: '1:t\ "3 f t 13_ Co 3, ~" lo. (() () 5 ~J 'v + (3 2 () 0~ ',;,' 1
ll ti"' 1111 q 11111 l1,11li 11 11 111 11111 lo 1 11d l h, 1 1,fll'lli, /() ~'. i 11 :l ' tj<1\' 1111~ ) :, 'l J Name: _ 11, lse Lhe quadralic formula to tlnd Lhc zeros. f (x) = x 2 Bx + 1 /.,(~) 1 fcky.l/(i){1) 0 Per: 12. Use the quadratic formula to find the zeros. f (x) = x 2 10x + 9 x '/ L 10)2Jc10)', yl1)l;) u,),\ \ 1\ ( ). ~ J / t,) ' \J 1 '/ l ( 1 '> > l :'> y v: ( )/ ) ('y' J ~' ( 1'/ l{iv 1'1 1. 'Jt' ' ' r ~ ~ 1..y.:1 1 ' 1 >' tv1', 15. Graph. f(x) = x 2 8x 7 vuf4e: K :_ j.f):. J_ :: 4 Lo.. ::,,') ~ ;nt' z..c,)..,z. :1 ~ (,LJ).,_ (4) =t v0' c~1, 1) i T t ' "' '10 ~ ; + ~ 1 ; i ~ : '.. 1!_, l ' ', 1 ' '. i ' ~ l : : ( J. 2
, 19. Solve the system of equations algebraically over the set of real numbers. f Y = 2x 5 ly= 4x 2 + 10x 17 2 0. Solve the system of equations algebraically over the set of real numbers. { y = 3x + 7 y = 2x 2 + 9x + 7 ::. z.~ z.... l 'Z,>... t0 c A x: _ti'.:t~~ 4N(") Name: Per: 21. Solve the system of equations a lgebraically over the set of real nu mbers. { y = Sx + 1 y = 3x 2 + Sx 11 ~ r e i ;::.. 3t 2. t~, ( ::;~A' o:::?,y2..+ o x ~ x.~ () rjco)...~l~i1 z) Z.L'7) X., ;.. Q j:: ~ "' 1( ::.. O.:!:~'l Q;J:l"Z,.:::'.:5' 1"2 = 0 b & / 22. Simpli fy each expression by using i. ~ i '\1 fj] C ' a i 4 ' <' ',.. "i). _,,,,.. ~~ 1. b. v 64 : f 'l :: [f.l C. s +../147 =5 + ~~ :;5' r i fi ffl {St+ ~ aj d. (2 + 3i)(4 9i) 25. List all words from the box that describe the number, 5 + 3i. 1 m r ~\, 17 " 23. Simplify each expression by using i. \ j6, ~~ ~; f0 1 C. 2 + V128 : 2+;) 2. + : _JT. Jz: {i+ ~ ~ ~ d. (5 i)(2 + 4i) = '5 ~.1 l ~ ( ~ r4d~ lo 'L ru,; _4; z. :: l D +f :" L/(1\ : 10 ~k'~ t '{ ::l 1~ +~ ~ 1 26. List all words from t he box that describe the numbe r, 19.5. C. 7 V243 : ""1,~ ~; =J d s",fi' d. (11 2i)(S + 3i) 1l 7, J;Cj10 ; '1")); t., '2. fi l5s w: \}; 3'?'i' lo~,._ L i;c; t 2 3> :' l,c1 27. List all words from the box that d escribe the number,../7. Natural Whole Nu mber ~ rrational r maginary nteger Natural Rational Numbe r maginary Whole nteger 3
Name: r er: 28. A ball on an unknown planet is 84 feet with an initial vertical velocity of 7 feet per second. ts h(t) = 7x 2 + 7x + 84, where h(t) ls t he height, in feet, of the ball, and t is the time the ball has been in the air, in seconds. L~~ co., ( c;~tj 29. A ball on an unknown planet is 60 feet with an initial vertical velocity of 48 feet per second. ts h(t) = 12x 2 + 48x + 60, where h(t) is the height, in feet, of the ball, and tis the time t he ball has been in the air, in seconds. ~ ~ \ '\> L '\,,~1K ~ 77\ y;: b. How long will it take for Ll&' the ball to reach the \..;;iu ground after it has been ~ tossed? Round to the 1,.3 o Ll nearest hundredttj.\ l 3 X:= 4 '.:tj ~'l. Lf(11,)(1.6) ' ~ ~ (_l'z) ~ u} $ 30. A ball on an unknown planet is 88 feet with an initial vertical velocity of 2 2 feet per second. ts h(t) = 1lx 2 + 22x + 88, where h(t ) is the height, in feet, of the ball, and t is t he time the ball has been in the air, in seconds. a, b, and c. 4l~c:cri' b. How long will it take for the ball to reach the ground after it has been tossed? Round to the, nearest hundredth. if y~ U~ J(ii,)t Lf(ll)M') ~ ~(,1\) ~ ~ y~~~j.j. )<J :;. 2,~ f4"y4,._..~;_ 22....)';:.. 2..2...± {q3 S b '"V) x :.:e.,u ~ 0 :: 1.! _ ~ ""271 i + 3:0'2... o.r J_.. >= '{ (Dr; ( 6/21 J c. ~ e maximum height t he ball will reach. ve,,,\~: /\ ~ l<? '2._ 2(11) 2).. 0 :.. ll ( l) "2. + 2 2L) ta f" ::. u( 1) t 7.:2_ + r "' = l ( 1vi... +.vr ::.. tf t Y t"' {f1 ~ 4
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