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fall08_3.3SupplE - 1%ka 11.05 — Supplemeui E(3.3 MW,...

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Unformatted text preview: 1%ka 11.05 — Supplemeui E (3.3) MW ,», i [(1’) : my" 7‘7 In + 4; re :_ 0 if) n, Quadratic Funmicui. The graph of a. quadratic, function ik‘ a, }:>a.ra.i_2<:>ia. their. i:>}‘><a>ne either Llp‘VVé-LI‘Ci or tiCfiYl'fl‘fEM'Li. if n, 11> 0 i the para,]:»<.>in.<;»i:>ens upward and Lhe vertex If (1 < 0 . Lhe pa‘i‘a,l:>olai opens downward and the is at the bottom of the graph. The I‘vi’inimum mine Vertex is art. the Lop of the graph. The R'Iaixhnum value of this function is the y chyrclinaie of Lhe vertex. of this. function is the y coordinate of the vertex. {XQ’} (Any) . . — , . i f . ”—12 The a*—coordn1a.te of the vertex is a: = 79—. The y—coordmam of the. vertex is y : f (7—) .11 La ’—-11 ,r__i \ The vertex is the point (— f( I) ) 2(1,’ 2a, . . a . ~15» The Equation of the Ame of bymmem‘y L8 .1? = -‘)—-. _.a. The domain of every quadratic function is (—00, 00). The quadratic. f unciion flit) 2 a3?" + ba’ + c: has range [k. 00) If a > 0 Where k is the y coordinale of the vortex has range (—00, Ir] If a, < 0 where Ir is the y coordinate of the vertex For each quadratic. f unction below7 find the Vert.ex,t11e AXiS of Symmetry, the y—Iutercept, the :1?-Int.ercept(s) (if any). Graph each function. State the. domain and range. State the minimum or maximum mine. 1. HM = ~2atz 4— 7a? — 5 2. Ha") = 3:0" 4» 21‘ + 2 3. H11?) = 41" —- 6.7.“ + :3 4. 5(1) 2 --161‘ + 481‘ + 8 [(1') =arz+2:r—-8 (j! ‘ 6. Na") 2 —:r” + 63? —— 23' 7. Ha") = ~37! + 21-4—6 R. HM: —2:r"'+ar+l 9. [(1') = -;r'“ 4— 4:1: - 4 10. H2?) = 21‘} + 8 (I‘GV'L‘SGd 8 / 08) MAC 1105 Supplement E - Answers 3.3 Parabolas The domain is (~oc, DC) for all of the graphs below. I. f(.7;) : ~2fl?2 + 7.7? ~ :3 2. f(.7;) = 37:2 + 2.7: + ‘2 3. f(.77) :: .7:2 ~ 6.7: + 5 7 . , T 9 7 v 1 5 7 .1 v " . \eitex (I g) \ertex ( 3 3) \eitczx (3, ml) 9 , 5 Range. (moo, :] Range [§,m) Range [~—4,oo) Intercepts: _ Intercepts: Intercepts: f :r: (rs-,0) (1,0) 3/: (0,—5) 1': None y: (0,2) 11': (1,0) (5.0) y : (0,5) Maxrmum of g Minimum of 3 Minimum of —4 _. 7—! 9 1 Axis of Symmetry: :L' 2 ~11- Axis of Symmetry: :L‘ = “g Axis of Symmetry: .7" = 3 4. 5(t) : —]6t2 + 481+ 8 5. f(.77) =1r,2 + 2.7: — 8 6. f(.7:) : ~77? + 6.7: ~ 8 3 . Vertex 3,44 Vertex (—1,—9) Vertex (3,!) Range (“om/14] Range [—9,oo) Range (—00, 1] Intercepts: Intercepts: Intercepts: 3 :i: V11 . , . 41?: (—5—,0) y: (0,8) 11‘: (2,0)(——4,0) y: (0,—8) :er (2,0) (4.0) y : (0, —8) Maximum of 44 Minimum of -—9 Maximum of 1 3 Axis of Symmetry: .7: = 5 Axis of Symmetry: .7: = —1 Axis of Symmetry: .7: = 3 W 7. j(:L) : -—.’l?2 + 27' + 6' Vertex (1,7) Range (-00, 7] Intercepts: a::(]:l:\fi,0) 3/: (0,6) Maximum of 7 Axis of Symmetry: a: = .1 R. f‘:(L') = ——2.7,'2 +1L" +1 9. 19 7,‘T..,' - — \er 9\ (4h) _ 9 Range (—00, a] intercepts: .73: <—;:—,0)(1,0) y: (0,1) Maximum of g . 1 AXIS of Symmetry: a: = Z f(:1:) = ——:L’:2 + 4.7;- — 4 Vertex ('2, 0) Range (—00, .0] l n tercept‘s: .7‘: (2,0) 3/ : .(0, —4) Maxim um of 0 Axis of Symmetry: .7: = 2 MW 10. j'(:1:) = 2:62 + 8 Vertex (0, 8) Range. {8, 00) :r intercepts: None y intercept: ('0, 8) Minimum of 8 Axis of Symmetry: :1: = 0 (revised 8/08) ...
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