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1 EOCT REVIEW UNIT 5 Quadratic Functions Name Kut Write each expression in factored form. 1. X2-2x - 15 (X>5')(X f 3) 2. X2-18x + 81 (x:-q)(x-q) (1)' (X, ) z- Complete each square and write the resulting equation. Then solve. 4. X2 + 4x = 6 (><"'1-):: r~ 5. 4x x + 8 = 0 xl+-tf)< Pf '-4-t/- )(f 2 = t:-jro K'). r 3~ -r'), =0 ( )( 1-2- )2 = I D ( X f 2- )2 = ~ ~ ~-- solution set: {-~ -CoI(!V [-2 110, -2 -r,;j solution set:~2-, - /} Choose the best answer. 6. A baseball was launched from a pitching machine that was placed on a platform. The height of the ball, in feet, is given b the equation h = -16t t + 9, where t is the time, in seconds, since the ball was launched. the term 85t? What is the meaning of ~ The platform was 85 feet high. ~ The ball was launched with an initial upward velocit of 85 feet per second..the ball was launched with an initial velocit of 85 miles per hour..,). The upward velocit is changing at a rate of 85 miles per hour per second. 3. 4x 2-25 (.If r S }(J,X -5) q tt 'K2.+3~"'7i -= -LI-7j (X ~i)~;:t )<. f ~ =-:!.[f.l.3.+ J.. )( T-;--L.L ~ x::: 2- -z:. = -:i.= I v z-..!- -! '" r- 2- x:" z-- 7. Which ofthe following equivalences can be used to factor x 8-8? (5) difference of squares, a 2 - b 2 = (a + b)(a - b) B. difference of cubes, a 3 - b 3 = (a + b) (a 2 + ab + b 2 ) C. sum of cubes, a 3 + b 3 = (a + b) (a 2 - ab + b 2 ) D. square of a difference, (a - b)2 = a 2-2ab + b 2 Solve each quadratic equation. 8. b 2 - lob + 2 = 98 b" -lob - q(p -= 0 2 -~lib f (b -/{:,){b rb)::; 0 6-/(,::0 br~=-o b e: II? h ;;. -I:> 9. 4c c = 120 t -/0 /3f C"J.f- 7" t: ~() C7--,.. 7" - 50 ::0 (C " I/)) (C 3) ;.{) Crlt) ~() c..3 ::0 c= -It) c=s - '10 Ī,t{o ZZ-IJ, '1,10 5,S>'

2 Determine an expression to represent the situation. 12. A penn was dropped off the top of a bridge that is 40 feet high. The height, in feet, of the penn t seconds after begin dropped is given b the expression -16t 2 + bt + c. The value of b, the coefficient of t is () tU.-1i5 r;irll,x.ti). so 1'tu..-tJ, la/17m Y!i()O I!J /$, The value of c, the constant term, is '10.-/he InifJ~ Au SA t: So, the expression for the height of the penn at an time tis -If? t,.1-40 Choose the best answer. 13. Which transformation describes how function f was transformed function 9 below? to create 14. Which of the following is true of function h graphed below? o B. C. D. Write an equation in one variable to describe each situation. Then solve the problem. 17. Y = X2 - X - 1 / -x=-l l;>!1;: X - J ;<'l_x-/;; x-i X").~)" ~ 0 X(X-1.) ;;0 -;'-:-0 ~:.2 g(x) = [(x + 4) g(x) = [(x - 4) g(x) = [(x) + 4 g(x) = [(x) The product of two consecutive odd numbers is 1,295. What are the numbers? /5f# X -37 a.nd --35 ZI'ld,*(xt2)EqUation: X(x+2) =/')..9<; Numbers: 35 and 37 /- It has no -intercept.. Its axis of smmetr is = 1. x= I ~ It has a positive leading coefficient, a. ID.llts vertex is at (1,2). 'I' l7 =rr- ~ fjca1 ~ tin-m- xl.f2-;<-12'1s =0 (x + ~7 )(X--35) ::,0 X r 37-=-0 -.J5-::0 X -:-37 X =~> 16. A rectangle's length is four more than twice its width. Its area is 160 square inches. What is its length? wtct-h,=i'in '1(2'1-+4) =j(po 2't~f4-X. ::-/t,() Equation: _X--,(,-2_X_.,_ l{-~),---=_/6,_0 Numbers: I') fh.::u) '-Y/; ~ x:. ".f- Z JC = [fo )(~f2.~ -;P:O ff'o)(x-8 =-1) Solve the sstem of equations algebraicall. Give the solutions, if an, as ordered pairs. X"" -/0 J B /J7) 18. Y = 3x 2 + 3x + 9 SOL-b17{)NS = 5x + 2 3;<1.r3x 1-1 ~SJ' 1':2-.3';(2-2)( f 7 ~ 0 a= :$ b ~ 'fa-c:: 1-'1(3X 7) b ':-~2- C ~ 7 :: -:FO ~tlr/1, MA.J ~() I. 19. Y = X2 + 30x [ 6x = Y + 44 =J!1 ;:u,~~44 X '11- ;0;< 1100 :::(Px- 41 )(,..f zt./- t- f /ti'-/ ~ 0 ( K f 12-) J,. : 0 X= -/2- (-/).J-II~)

3 r: The table below represents a quadratic function. Use the table for question 20.!i6-~~ ~I I~ z 1{-3 I /I-~ J I;rx) I ~1 I ~O I!s I ~6 I!3!--- - I /-1) 20. What is the average rate of change for the function on the interval [0 3 What is the average rate of change for the function on the interval [3, 4]? _Z-=' What is the average rate of change for the function on the interval [0, 4]? _'...:.,2. _ '------> _ 21. The graph at the right represents the function t. A second function, g, is represented b the equation gex) = 3x 2-3. Compare the following 'tla-~chc- - ke features for these two functions. {z} X-.-t"nt. (-1.0) Identif and compare the x- and -intercepts, ~~ ifan.~) ~ ~ ~~~ ~~ (I,D) ~ tf"a..dnvhc.- - boh1 ~~ PtJOIr-VPI (I ),,1>1'" Identif and compare nd behavior. t2f ~ fp.'yp&.cn!~~-6--+.' ' nt., ez-/}vc- 00/ '}{l< C-f>pr-pt:-~ ~ (t7#-~) -A~phl tm - as X.(?f'.eroadu4/ - 0-0,.I'(~) #frfrl~hol a'i'::ge va ue ~lx,~c a?r;;! cfo~it~1 FCr)cpl'fl7G(;h.co f-~ (I) X/W1.:C) function has the greater value? How do ou know? --.1-, --ti r-f i ('i,o & Uf?rnt,uf/at fu'" C/7 M."., Both 1v11CI7~;. 9 ' i'1t, rn. L ~ ) In(tt c PO 1a/:;f - r6~. '''tlup~'t:l fruncnm I ~ ~ (0,-2. ;t-{/lwt:! t:u: fjy:jt, bur"/hen I'J4AA("~ me?- -c, r~ P.J ~ VtW.tL- ;(. II1Crf'"~ Use the function [ex) = 2X2-2x to answer questions 22 and Write the function in full factored form. /(1-): 2(YZ.-)< - 72-) -= }. (X - qxx.f~) 23. What are the zeros ofthe function? - r a-vtd '1 Use the information below to answer questions 24 and 25. The height of a ball thrown from the top of a platform can be modeled b the equation [ex) = -16x x - 34 where [ex) is the height ofthe ball, in feet, x seconds after the ball was thrown. f(x) =- -/(p (X '-- L-/'K rtl ) - 31.fb'l- 24. Complete the square to write the function in vertex form. -,-i->.(-,-j(~j'-~ -"':"/"":"(p---'-(j-x_---,2:::::';;,l-)_2...:..f--=j::...:d", Find and interpret the coordinates of the vertex and the maximum of the function. _ c 1:= (2 UJ,2~dtY

4 Graph the function on the coordinate plane. Then identif the intercepts and maximum or minimum for the function. -intercept(s): (Oth) -::-f ('f) f r?' ~\;: ').rfr x-intercept(s): (-2JO ~a('i()j ~ b maximum: minimum: f ' - ~ (X - 2-) '1 f? : 0 -~ (X-2)~ ~ -8' r> 26. [ex) = -~ex - 2)2 + 8 f(o) -:;-~ (O-Z)" (x- 2.) ~:. X-2=:t'/- l(p 27. Which of the following inequalities is graphed below? v A. Y > ~X2-3 4 B. Y < ~X2-3 4 C Y > ~X C0 Y s ~X The owner of an orange grove found that the number of orange trees planted per acre affected the total number of oranges produced table. in that acre, as shown in the Number oftrees, x Number of oranges, f(x) 20 12, , , , ,320, , ,400 Which of the following quadratic is the best model for these data? A. [ex) = 47.1x2 + 13,535x B. [ex) = -47.1x2 + 13,535 (E) [ex) = -12x x 'r{ [ex) = -12x 2-887x = 35.7

5 29. A coin was dropped from the top of a bridge that is 100 feet high. The function that describes the coin's height,, in feet, x seconds after it was dropped is = -16x A graph of this function is shown on the right. Based on the context of this question, what are a reasonable domain and range for the function? o 5 X ~ ),5 L 0/ /ooj 30. A baker sells cupcakes for $3 each. Her revenue, in dollars, is modeled b the function Rex) = 3x, where x is the number of cupcakes sold. Her costs can be modeled b the function Cex) = 0.02X x + 50, where x is the number of cupcakes she sells. The function to model her profit, in dollars, P, can be computed b subtracting her costs from her revenue. Write an explicit equation for P in terms of x, the number of cupcakes she sells.?(~):-o.02x ~ d,5x -50 P{X); (){X)eC(;x) e 0 > ::: 3x ( J( O.02 ~~ I- 0.5)( j. $0) z: -O,02x ~ I-~SX - 50 /

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