Review Quadratic Formula, Cornpletinq.Square and Quadratic Applications

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1 Name_g_jf ' period _ Review Quadratic Formula, Cornpletinq.Square and Quadratic Applications,! 1. The John Deere company has found that the revenue, in dollars, from sales of heavyduty tractors is a function of the unit price p, in dollars, that it charges. If the revenue R is 1 2 'i R(p) = p +1900p, 2 Ca. What unit price p ShOUld,be char,ed to maximize revenue? J qb() Zft '1D5 D DO b...:.l q.!.:6:.:::::0:: YZr.;;..(v_:to_()_)_z+ q _0b,( ) b. What is the maxi um revenue? I...l. Vfj! p:;}cf6}? _ 0,..1 [Z(/960) ::/,P6SP"6 r() (Yz) '01 IDvJ "'_.J r > 2. The height of a fl re fired from the deck of a ship in distress can be modeled by h = 16/ +104t + 56,where h is the height of the flare above water and t is the ti me in seconds. Find the time it takes the flare to hthe water cjoiq Ii.Qd. Po ("/"II. Ltiq r5e (JX1d.s J 3. The height of a rock thrown off a cliff can be modeled by h =16/ 8t+120,where h is height in feet and t is time in seconds. How long does it take the rock to reach the ground?,... ) t=qcto y G'r ' qucujvef1c tot'mtf( 4. Water is shot straight up out of a water soaker toy. The quadratic function y = 16x x models the height in feet of a water droplet after x seconds. What is the maximum height of the water droplet? 'I ' 1/ C ) z, +(J) :It3 '' J ver,ex Z( 0) rr;r:: ] (XCJ J :lto. 5. A group of friends tries to keep a beanbag from touching the ground without using their hands. Once the beanbag has been kicked, its height can be modeled by h = 16/ + 14t + 2 I where h is the height in feet above the ground and tis the time in seconds. Find the time it takes the beanbag tof;;/; uodrdl, h) (yy <Alet 05ec»:;]

2 6. The height of a diver above the water during a dive can be modeled by h=16/ +8t+48, where h is height in feet and tis time in seconds. Find the time it takes for the diver to reach the water. J,.. s7"77 fadorov q (,(YMwt;. 7. A fireworks shell is fired from a mortar. Its height is modeled by the function h(t) = 16/ + 224t, where tis the time in seconds and h is the height in feet. a. If the shell is supposed to explode at its aximum height height shoull.lljt'tfoq1et"= )( ddj e,,+e: 1h61h 1B lco) h (1):")1,t6'Z4(1) feetb. if the shell does not explode, how long will it take to return to tround? Co*'2. + Zlltt ::;0 r. Q do (". I (ot ( Ilf)O IT ] tc:c{ J::::Jt/J llf5ewv1d 8. The product of two onsecutive odd integers is 99. Find the integers. p;;t:, J XC').. T"6) = Cfcr y. 9 noi :: x+ i Z4:2qq i =6 + d = 1 z ('/.t'ii) C...q') d),' i :: /l f97 9. The longer leg of aright triangle is ten less than three times the shorter leg. The hypotenuse is 4 more than the shorter leg Find the length of the shorter leg.

3 10. A square field had 3 m added to its length and 2 m added lsto;uit i...w.u:llll.} then n:t. had an area of 90 rrr', Find the length of a side of th ori' field. C!J3){)o;))::;9a ('It/Z)(K;1)r6 'Ii:77.' x.zt5jtfco=.90 Jle,rg th X )G 2t5x.rf::.D W 0.+h X:Jd Cl!!!.J 11. The length of the diagonal of a rectangle is 3 cm more than the width and the width is 9 em less than the length. If the area is 580 cny2;frnathelength of the rectangle. (i... q) 5tfo (J2;:A) (flt20) ::6 di. wt s.z.j'386::.6 ['),971 Jb +l ct, ',. '. lot +h: 1.'. ;29Cfl J 12. In an isosceles triangle, the base is 5 m longer than the length of one of the equal sides, and the altitude is 2 m less than the base. The area of the triangle is, rrr'. Find the length of the base and the altitude of the triangle. L1 (i+5)'0+) ::31/, 5 ()!3:){fr.2)=6,!:=:.====_ I" j. ztj'x1:()::..7j'j j..3:2m bq L x+5 L... /J /)0 Or e ::.. (X+5).:J /v L +,YJ 1fol:.o YJQS.. ( M O,.U'lm t'. C1lt1+uut e..:;;n,... Findt e iscriminantand state how many RealSolutions. 'L.. 'f. 7k, 4X+8 =0 13. _X x 2 +6n6 =7 [ IW) ' W (I)(9) qy''+ l,j + Discriminant L G>? # of sotutlons ;;;2 r ec...t Discriminant 0 # of sotueions lrto.o 15. 2x 2 8x4'=4 '2:i z"./f iif 6 Discriminant 6 # Of soiucrons e:»

4 Write the following in vertex form. ",. '.. Solve the following 19. 9x 2 18x57=6 by completing the square x 16x+22=5

5 8 =0

6 " (3" /wt:l5b +l'jo =0 ( ;2t 2 + ( L 5) 0, I/ P1/(:J f:: 2.+ (Pi) 5 t LS')) c 0 l'..., ",, 9J ( ;)t:(l +3 5(t+3) I=.O ;00... ", p) t5 (t +3)::. 0 t :. I:: : :3,. "...! (4UX:3:< (j = (l ;ll)l+3)(i) r: (P ') 0 X =. I fa 0 lo J J r: ('" /GtL. l/4t id::o./ ;) { R t 2 1l ::..0,, d/8 t <. t tit. Il ::. () ';,;I J t (+ 1l±TI t 1)' ().. "? /'./ '" (t+l) ti):..o " ) I f=:j, ",j

7 »<>; ({Q J (lo2+p)t. +4AO '" 7 /) C 2. e )=O ',/ p) / /:) I: 2 4 (r 3 t: (o)l./"... J/ Wf; (&'2) +.3(62)' ;.,..:;. ''A 7d t; +) (1:; 2) : () " if :..:J _ /7j) '/224 h (l) I (0 l 7'5"L +J) If( 1)..., ""' 2 (I (0.., n(i):' 14 X '1.... " r.: It o t; 2. +J.dut::: 0 <c:»: " {Gt(4)O f 14,,.,. r

8 cwtx(o l47 i (0) o,," = / "' "'(_Igi t4 )(Y(a) =.() J " Q'i If IIF==:=.J:=::::::+;:;tf::::J1 l {' I bi wl.' II"

9 @ J z,jirj rt ( i?) 2 2 (gs1 eo't ('I 2 :::If 9 () (xj)g+lf 21<24,( i5}::o V 3 3 X ;!?X t (4 ) z. + I /'" ;j 3 < _{}_ (,/ 4) z. ;53 't a? l' '3+ C:3}( jlf) Z = :5.. I

10 iff) i2 :2 V "7 l r t L id)c +(0 L, = }tl, ()(+/Y S+f 3 q (1' +1}?:7(9,) ():: q (tl)"2.j;j,,... " ', ", " '..".

11 I Ir.

When factoring, we ALWAYS start with the (unless it s 1).

When factoring, we ALWAYS start with the (unless it s 1). Math 100 Elementary Algebra Sec 5.1: The Greatest Common Factor and Factor By Grouping (FBG) Recall: In the product XY, X and Y are factors. Defn In an expression, any factor that is common to each term