{Q, f(x) = 3x2 x+4. U2D10 MCR3UI Worksheet Systems of Equations Involving Quadratics. 1. Determine the point(s) of intersection algebraically.

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1 ) f(x)=2x2sx+2, g(x)=6x1 c) f(x)3x22x1, g(x)=x6 b) f(x)2x21,g(x)=3x+1 ) f(x)x2+6x5, g(x)=4x Deermine he poin(s) of inersecion lgebriclly. 2. Deermine he number of poins of inersecion of f(x) = 4x + x 3 nd g(x) = Sx 4 wihou solving. 3. Deermine he poin(s) of inersecion of ech pir of funcions. 4. $3or$4 5. k From 11: m, unil 3: p.m seconds fer he firs prchuis jumps (2.5 seconds fer she jumps) 2. one 3. ) {Q, 7. )y = i 16 b)y = 2x +b,h > 16 c)y = 2x+b,b <16 8. ) ((2,1), (5, 2)) b) ((1,3), (1, 5)) ((,ll)} c) d) no rel soluion 9. D > so hey will inersec. e) [Li + c, 15 (i is + 4 J)j f) {(6,3), ()} c) no inersecion 8), (7, 43)) b) (+T 43+cTh) (i_vth 43JTh)) Answers: 1. ) ((4,3), (6, 5)} b) ((2,7), (, 1)1 c) no inersecion e) h(x)=2x2+3; g(x)= x22x+7 flh(x) =2x2 +24x69; g(x)= x2 lox+27 c) 12x4y=19; y=3x212x+14 d)2x3y=6; y=3x2 +24xS ) y=3x; y=x28x+13 b)g(x)=4x1; f(x)=2x2+4x+1 ) Once b) Twice c) ever funcion f(x) = x(x 6) seconds is modelled by he equion y = A second prchuis jumps 5 s ler nd freeflls for 1. The UV index on sunny dy cn be modelled by he funcion f(x) =.15(x 13) where x 11. A prchuis jumps from n irplne nd immediely opens his prchue. His liude, y, in meres, fer UV index greer hn 7? srigh ph on he sme plne s he seroid ccording o he liner equion y = SOOx A spce y = 6x2 37x For he period of ime h i is in he sme re, spce probe is moving long represens he ime of dy on 24hour clock nd f(x) represens he UV index. Beween wh hours ws he f(x) = 3x2 x Deermine he vlue(s) of k such h he liner funcion g(x) = 4x + k does no inersec he prbol excly one poin. gency needs o deermine if he seroid will be n issue for he spce probe. Will he wo phs inersec? 5)2 few seconds. Her liude, in meres, during his ime, is modelled by he equion y = 4.9( + 3. When does she cch up o he firs prchuis? S. Deermine he vlue of c such h g(x) = 3x + k inersecs he qudric funcion f(x) = 2x2 Sx + 3 he producion o brek even. in dollrs. The cos funcion for he producion is () = 6 So. Deermine he icke price h will llow 4. The revenue funcion for producion by here group is R() = SO2 + 3, where is he icke price 7. Deermine hrough invesigion, he equions of lines h hve slope of 2 nd inersec he qudric 8. Solve lgebriclly. You my confirm grphiclly. 9. An seroid is moving in prbolic rc h is modelled by he funcion c) f(x)=5x2+x2,g(x)=3x6 b) f(x)z3x22,g(x)=x+7 U2D1 MR3U Workshee Sysems of Equions nvolving Qudrics

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