Section%202.6

Section%202.6 - ll / l ‘3 lad) <9 8’ MA 180 -...

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Unformatted text preview: ll / l ‘3 lad) <9 8’ MA 180 - Precalculus Professor Terry Section 2.6: Quadratic Functions E Graph Quadratic Functions of the Form f(x) = x2 + k Graph. Label your graph. Complete the tables. Vex/Jorch I CM? Observations: ‘ Y a We, 3 , MVP 3 L/th's L9 5 W C I d am 2 wst Graph Quadratic Functions of the Form f(x) = (x — h)2 Graph. Label your graph. Complete the tables. 2 y1= 3‘ y2 = (3H3)2 J’s =(x—1)2 Observations: h 0"“ meslago: g... INCA/1a j. lth suds“, MA1808ec2.6FaII05ewt I 5.)) WU£ (jl pkg M I . Gragh Quadratic Functions of the Form f(x) = ax2 I W L3 ~ vm Graph. Label your graph. Complete the bles. Observations: V‘ w Cg‘fire J; (a a Veu (blw {lie/(m I (j 32 VMCCLQ ‘ {SS Gra h uadratic Functions of the Form f(x)= a(x —h)2 +k 6g i Graph. Label your graph. Compiete the tables. Y-intercept(y2): xr—O 8 I ‘ [(9 _ i ' X-intercepts (Y2): ‘3 3 0 (03% I O) 0 2 -— 5 ( X-E 231+ ; flaz—aOHa)? .i 93 23H; % 20¢”); } __ 7, _ —.‘ E Write Quadratic Functions in the Form f(x) = a(x — h)2 +k Standard Equation of a Parabola with Vertical Axis of Symmetry The graph of the equation y = a(x—h)2 + k for a :t 0 is a parabola that has vertex V(h, k) and a ‘l vertical axis. The parabola opens upward if a > 0 or downward if a < 0. /—\\ If f(x) @then by completing the square on the variable x (x) = a(x — h)2 +k. if a quadratic function is written in the form f(x) = a(x — h)2 +k, the vertex is l". k . Find the vertex ofy=x2_6x+11 / v. . . 1-1 a) Complete the square of the binomial x Q41: \ i 31(‘GB: ‘ :33 y=x2-6x+___cf__+117{j_ dug y=(X-_32__)a + I.) (73).?“ : (T y: (X‘__ ‘t 9 \K:_ertex= C5, b)Axis of aymnwetryisx= c)x—intercepts: 0 1 (X‘ajz—f Q x 2 5i LIV/fl extra mi it fifyséfv‘gp l 3410 %:ll Gal“) 'X IO ii 3 3? Co ll 9) Check using a graphing utility. / MA‘IBO Sec2.6 Fa!|05 ewt ’\ 5 Find t e vert of f(x) = 5x2 +20x+17. Sketch the graph. / £7) 2 i '11 ‘55“ "1 @ti't5’ £00 ~ 5 5 TQM : 5 (ma? -— 553 ""” WW“ win—20 *5 M fi’vaafi (0in orSX1+20x+t7 ‘2 ~ X2, —wi\/tioa—~i(§¥§3 O W ‘1??? *1” W Derive a Formula for Finding the Ve ex of a Parabola Theorem for Locating the Vertex of a Parabola: The vertex of the parabola( f (x) z ax2 + bx + c has x— coordinate —i and ordered pair [ é:— , ] 2a 28 Use the Vertex Formula to Find the Vertex of a Parabola Find the vertex of y = x2 — 9x + 8 a b ‘aZQV—ciK'E/M? 2' Z “a 2 (RI a 3‘ 19:"? X: “('43 g H {:4 13:? C23’ 2Ci) ‘61—?"f'q, _,,_ i ~13 X235. (6: “HQ? “f Find the vertex of y=—x2+4x—4 2. ' __‘ Zwi x133 \32_(q,) we) 4 101% _X:——‘-i {jZ-L(~+?{"1L C= “Li 2C“) O X 2 52 2 MA1BO Sec2.6 Fal|05 ewt I L; L O > E] Find the Minimum or Maximum Value of a Quadratic Function In CMKW f3 1 /Ve/\7\'zic B I i 2 y of gasoline at a speed of v mph is given by 1 5 for M12470. M =——v2 +—v 30 2 ‘ ' a) Find the most economical speed foratrip. \/ ‘1’— aq Moot phi;ng m - - -— 573 \1‘ Quiz); V ‘1 - _‘ I 2 u g/ 2 9 Q 7303 rim * a “ -—.~ 2 Ifth _ s 7 .6 hj b) Find the largest value of M. . ;%fl_ .. -; '19 l e“ ’T‘S‘ m '" 30(‘3/ 't ‘2: mlééuims Flight of a projectiie An object is projected vertically upward with an initial velocity of vo ftlsec, and its distance 300 in feet above the ground after 1‘ seconds «he» 9 Q: is given by the formula 50‘) = #169 + vat. “A‘s a) If the object hits the ground after 12 seconds, find its initial velocity v0. 5(a)?— C) 505:" Mil-1V0} . 78013: "ibgadlal- V0 ((7,) 2 O Vo(lz/\: 3304 an;th vamp-o _ v0 :- 330“! b Find its maximum distance ethe round. in “.1 Q ) 8 {ff%;:fi‘i?fii IVO z 6% eh . f” . fl (0 20’“ twitc- 599? ’MWHMQ < _ 2 2—; \r X F(é)zgqb i? ale; k}: r 2(_H’) / . MA1 30 8802.6 Fall05 ewt A quadratic function is a function that can be written in the form f(x) = ax2 + bx + c, where a, b, and c are real numbers and a i O. w l "Lp f(X)=X2 f(X)=aX2+bx+c, E—O/ f(x)=ax2+bx+c@ b: o OP-éncp Qr‘LQ we: (imam, C 2 0 Q2] Vertex 15' m \OWC%‘§F Qi/ 9V) ‘ "Du grafiah 65; wwpwfl Axis of symmetry MAT 80 Sec2.6 Fal|05 ewt ...
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This note was uploaded on 04/25/2008 for the course MATH 30191 taught by Professor Terry during the Spring '08 term at Montgomery.

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Section%202.6 - ll / l ‘3 lad) <9 8’ MA 180 -...

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