# H x 2 x 2 4 x 1 10 9 8 7 6 5 4 3 2 1 1 2 3 4 5 6 7 8

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10.) h(x) = 2x2+ 4x+ 1-10-9-8-7-6-5-4-3-2-112345678910x-10-9-8-7-6-5-4-3-2-112345678910yVertex: _______Max or min? _______Direction of opening? _______Axis of symmetry: ________Compare to the graph of y= x_________________________11.)k(x) = 2 – x12x-10-9-8-7-6-5-4-3-2-112345678910x-10-9-8-7-6-5-4-3-2-112345678910yVertex: _______Max or min? _______Direction of opening? _______Axis of symmetry: ________Compare to the graph of y= x_________________________12.)State whether the function y = 3x2+ 12x 6 has a minimum value or a maximumvalue. Then find the minimum or maximum value.13.)Find the vertex of 21572yxx. State whether it is a minimum or maximum. Find that minimum or maximum value. 22 24
Another useful form of the quadratic function is the vertex form: ________________________________.GRAPH OF VERTEX FORM y= a(xh)2+ The graph of y= a(xh)2+ k is the parabola y= ax2 translated ___________h units and ___________k The vertex is (___, ___).The axis of symmetry is x= ___The graph opens up if a ___ 0 and down if a ___0.Find the vertex of each parabola and graph.13.)212yx-10-9-8-7-6-5-4-3-2-112345678910x-10-9-8-7-6-5-4-3-2-112345678910yVertex: _______14.) 21153yx -10-9-8-7-6-5-4-3-2-112345678910x-10-9-8-7-6-5-4-3-2-112345678910yVertex: _______15.)Write a quadratic function in vertex form for the function whose graph has its vertex at (-5, 4) and passes through the point (7, 1).kunits..5
GRAPH OF INTERCEPT FORMy= a(x p)(xq):Characteristics of the graph y = a(x p)(xq):The x-intercepts are ___ and ___.The axis of symmetry is halfway between (___, 0) and ( ___, 0) and it has equation x=2The graph opens up if a___ 0 and opens down if a___ 0.16.) Graph y= 2(x 1)(x 5)-10-9-8-7-6-5-4-3-2-112345678910x-10-9-8-7-6-5-4-3-2-112345678910yx-intercepts: _______, _______Vertex: _______Converting between forms:From intercept form to standard formUse FOIL to multiply the binomials togetherDistribute the coefficient to all 3 termsEx: 258yxx From vertex form to standard formRe-write the squared term as the product of two binomialsUse FOIL to multiply the binomials togetherDistribute the coefficient to all 3 termsAdd constant at the endEx:2419fxxHW #15: Pg. 202: 47-63 oddpg. 240 #3-39 x 6’s pg. 249 #4-40 x 4’s6
Notes 16: Sections 4-3 and 4-4: Solving quadraticsby FactoringA. Factoring QuadraticsExamples of monomials:_______________________________Examples of binomials:________________________________Examples of trinomials:________________________________Strategies to use: (1) Look for a GCF to factor out of all terms(2) Look for special factoring patterns as listed below(3) Use the X-Box method(4) Check your factoring by using multiplication/FOILFactor each expression completely. Check using multiplication.1.) 2315xx2.) 2624x3.) 2524xx4.) 22581x5.) 222121mm6.) 24129xx7
7.) 25176xx8.) 23512xx9.) 25t2110t+ 12110.) 21636x11.) 294249aa12.) 263336xxB. Solving quadratics using factoringTo solve a quadratic equation is to find the x values for which the function is equal to _____. The solutions are called the _____ or _______of the equation. To do this, we use the Zero Product Property:Zero Product PropertyList some pairsof numbers that multiply to zero: (___)(___) = 0 (___)(___) = 0(___)(___) = 0(___)(___) = 0What did you notice? _______________________________________________ZERO PRODUCT PROPERTYIf the _________ of two expressions is zero, then _______ or _______ of the expressions equals zero.
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