2.2 - 2.2 Quadratic Functions Recognize characteristics of...

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Unformatted text preview: 2.2 Quadratic Functions Recognize characteristics of parabolas. The Standard Farm at a Qanflratie Fanatical-n the quadratic iflltifiiiflfl m nix W 5}}: + .5; ti rfi {J is in standard form. The grant“; {at f is a nai‘abnla whose vertex is the point (in it}. ‘itte giammsia symmetric with respect in the Jim: .9: w in its :1: it}, the parabola. one-as upward; if a 4: lit, the paranoia opens downward. Properties of the Graph of a Quadratic Function M? + bx "Jr" C a :29 i} {7 . A b ‘ . . . Vertex. m ( Am ot symmetry: the 11m 2c! 2c: l) ~ 2a Pm‘zdmia opens up if 42 T.» U: the vertex is 2': minimum point. Paraimla opens down if a «t. 0: the vertex is u, maxnnum point. Graphs of a quadratic {mnctimm fix) max} —l=— bx+c,a #0 Axis of Vettex és c7 symmetry highest [:30th Q, _?\3 Vertex is. Axis of lowest point symmetry {a} Opens up (in) Opens down a :23} U a a: 13 Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=—3x2+5x—4 a 1 ,3 2 L5” C 7; -" LI. Graph parabolas. (3L The Mntercepts af a Quadmtic Function 1. If ihc discriminant I33 w 41:6 TH), the graph of fix) 2 (if + bx w+» (' has two distinct I~imcrccpt5 5'0- it‘ Misses the. xwaxis in two places. 2. If the ailscnn‘unani b“ — 444‘ m (L the graph 0f fix) 2 ax: + 1n: + c‘ has one .1”—ifl[é‘[‘C(3le 50 it touches the .r-'txis at its vericx. 3. If the (imcrzmlnmti b” m 436 «I; {L the graph of fix) 2 ax: + bx + a“ has no Animate-pt 80 it (1100:; not. crew 01' much Um l’leiS. Axis of symmetry 0 Axis 0f Symmetry Axis of symmal‘r‘y x m. p X 7.x; 2a 23 V st'ntercept b D (— 27 v f (- 5)) (a) 02~4HC>0 (b) 52_4aczo Two xvmtercepts x-intercept X (a) b»? a 436 < 0 Una X-intercept No X—intercepts Gmphing Qifififlfiifit Funcifiam with Eanfi-{lm in; Smasde Farm: Tm gm;th flail r: m" K 3:33 I' if. L Thiamine whmlaea‘ am Wmmm wens upxarm‘é m' dim'nwardfl ff :1; .I-N [L ii: twang Lipwaré.. Ifa {7h i1 gyms; d-uwtiwartf‘. 2'... imagine tiring wr'tax scuff the parefim’éaflhc warm: (i5; (fig. 32'}. .3; 15511:? Eli’s}? x—z‘mfimapm by miving f1}: 1;} m U. Thai: fura—a:£im1“&matzcms arc the xintarceyts, 4. i-"imf the: y—ézzicmapt by campuiing {{6} i. Pia: .the: int-awepm the varies??? and additimw] gmirmtx as; mammary. (“mama thaw {minis wiila 2i gnu-math mwc: mm is ghade film :3 mm Graph-in ;_ £31.: Bum-tic. Fanatiéns with Equatisafia it“! than iFtéfi’i’i $41] = a}: +552: 4- at: T1:- ggraphfsng :- m: + a; ~i= c: L mmmg Wham: the gimbals gigs-em upwmfl m dwmmfla I]? a {L 1'1: ugzema u mum!“ 3113 a «a: I). it gyms azlszswnwaird. . 4 . . r" g“; f g, “m 3; 53161311313113 the mitt-3;: tithe pambelaféfiw Ewe: l5 w .r' m —| ]. fl 4213 ‘ a Em 5 3L Fiat} fififg' x-jmampra by Enlarging fix} an 11 The: 33311 Hummus Inf m‘ + {3.1 + r: m I3 am this x—ifitfitfipfi, ii Fififl the; Mmempt amputing; 1133;. fifi] :- larm in 311132: fiamti-mig aquatimfi, 1:113 y-jmvamgft is thraugh [-13, E}; fiat “Irina Hamlin; ma 11:51:31. am afljjtifluaj [mm m lawman}: lfmmnea may? paint? with :1 331in films. :3 {the fifli'fléiftflfil mm pmabanlxa gnaw Sketch the graph of the quadratlc functlon. f(x) 2 6 «5x + x2 Jr 3ch cm Von/1M CW1 '01”; C“; (him) :3 k : XI::Y\C:&0:E X: “2% Tb M : “‘ 0g) 1 5—: L 1U) ‘3 J k: “kc/06%”; “" ,_ '1,“ 6‘ 13> W W Hag): é b—g—w—L “ (W; .- sis-l“ 3w ,411; : _____ 4 o X" 2. 3/ 71km”? : Lr Fr‘ncl “IR; V’fflJMCfl—Pwl is pom >030 Mace/3+5 7%): wwwol I 6 Determine a quadratic function’s minimum or maximum value. a‘fiutmum and Martimam: Quadratic Fang-tiara. Consider qua-draiicfuuctivn fix} W {2.152 ~§~ 35:: wt“ c. l. H a 11"» it than 3‘ has ammlmum that {mama at .1: ’" mg—tTi’EES minimum . . ' a r” value 155 g . - . . _. 33v . . 2. fit; "-1 ti. than f liar; amammam thatoccurs at .2; m This: mammam I . ‘ £41 , f} value 15; f( "in as: ch cage. tha value: of. I gives; this tantrum} of 113% minimum or maximum value. The vaiua at y. ar f ~ \ 3), given that minimum or maximum vaiun. it For the quadratic function, f (x) = 4x2 — 8x, a) determine, without graphing, whether the function has a minimum value or a maximum value, ,—- I b) find the minimum or maximum value and determine where it occurs. c) identify the function’s domain and its range. @ PDQ C 0a.,ch Q > 0 i‘QL$ 0* hmtn [mkkm V‘Q Cg) TO "iko. Merli‘m‘vbm VOLLA'Q— ‘r ab 61:” b:_.% CLO '2_Ou : fl :: —C_‘;5—-:—i an) 8‘ 4. Solve problems involving a quadratic fimotion’s minimum or maximum value. Strategy for Staining Prohiems iamsaieiflgflaximieifig or nil-inimng Quadratic Funefions Read the. mum carefully and {lesion whieh Quantity tetra-1m maximisfied or minimized 2. "use the conditions- an 51:13:: prubiam to» express guaranty; as a inaction in one variahie. ' - 3, Rewrite theiducfimiin the term fix} =‘ 421553“ eh ism elm cu éL fiaieinate {sign-:3? 135'-}i‘lfifieflifimimmfli 2:.- --~ ——_—. fia-as-ussnnmum _ 2n .‘ .. '. --- _ . L. .- . i .. .,.. ‘ vaiue 13 f? “'12— .if a a1 {35 f has-a maximum-m: 2: == -—,—1EI-.. mammlun '3 u: - LI- Vaiéiue is 5. Anewzer Ehé-~Qflfi§fi§lifi.fi9&3fl in am premiering. You have 64 yards of fencing to enclose a rectangular region. Find the dimensions of the rectangle that maximize the enclosed area. What is the ’maximum area? 3—2—15“? Among all pairs of numbers whose sum is 50, find a pair'whose product ' as_possible. What is the maximum product? + E, I, 5‘ O >< ooh—x) ._X7—+5‘0X' ‘ " graph Liam Cale-Gpifiy“ X3 2-; mexX‘imu/m . ' l I I Za—ZX “K; m) Auk/ML : X 20 V40): X-(Zo PZX) P 9. — ~—7_X +—o‘lo><‘ or (Effie! X5 FAD-— 2A x 2 “2° : 2(«;) .: —— 2L2?) +107) 2 —— LID—Hero : 6—0 Ora-$3 S’emtfimfiI Mammwm We. : 50 1:0ch ...
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2.2 - 2.2 Quadratic Functions Recognize characteristics of...

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