A Practice Understanding Task
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1 46 SECONDARY MATH II // MODULE Lining Up Quadratics A Practice Understanding Task Grapheachfunctionandfindthevertex,the y"interceptandthex"intercepts.besuretoproperlywrite theinterceptsaspoints. 1. = ( 1)( + 3) 2. = 2( 2)( 6) LineofSymmetry Vertex x?intercepts y?intercept LineofSymmetry Vertex x?intercepts y?intercept 2013www.flickr.com/photos/sandyleee
2 SECONDARY MATH II // MODULE 2 3. = ( + 4) 47 LineofSymmetry Vertex x?intercepts y?intercept 4. Basedontheseexamples,howcanyouuseaquadraticfunctioninfactoredformto: a. Findthelineofsymmetryoftheparabola? b. Findthevertexoftheparabola? c. Findthex?interceptsoftheparabola? d. Findthey?interceptoftheparabola? e. Findtheverticalstretch?
3 48 SECONDARY MATH II // MODULE 2 5. Chooseanytwolinearfunctionsandwritethemintheform:() =,wheremis theslopeoftheline.graphthetwofunctions. Linearfunction1: Linearfunction2: 6. Onthesamegraphas5,graphthefunctionP(x)thatistheproductofthetwolinear functionsthatyouhavechosen.whatshapeiscreated? 7. Describetherelationshipbetweenx?interceptsofthelinearfunctionsandthex?intercepts ofthefunctionp(x).whydoesthisrelationshipexist?
4 SECONDARY MATH II // MODULE 2 8. Describetherelationshipbetweeny?interceptsofthelinearfunctionsandthey?intercepts ofthefunctionp(x).whydoesthisrelationshipexist? 9. Giventheparabolatotheright, sketchtwolinesthatcouldrepresent itslinearfactors Writeanequationforeachofthese twolines. 11. Howdidyouusethexandyinterceptsoftheparabolatoselectthetwolines? 12. Arethesetheonlytwolinesthatcouldrepresentthelinearfactorsoftheparabola?Ifso, explainwhy.ifnot,describetheotherpossiblelines. 13. Useyourtwolinestowritetheequationoftheparabola.Isthistheonlypossibleequation oftheparabola?
5 50 Name: Ready, Set, Go Structures(of(Expressions( 2.8( Ready Topic: Multiplying binomials using a two-way table Multiply the following binomials using the given two-way table to assist you. Example:))(2x+3)(5x 7) =10x 2 +x 21 ) 1.(3x 4)(7x 5) 2.(9x+2)(x+6) 3.(4x 3)(3x+11) 4.(7x+3)(7x 3) 5.(3x 10)(3x+10) 6.(11x+5)(11x 5) 7.(4x+5) 2 8.(x+9) 2 9.(10x 7) The like-term boxes in s 7, 8, and 9 reveal a special pattern. Describe the relationship between the middle coefficient (b) and the coefficients (a) and (c). SECONDARY II // MODULE www.flickr.com/photos/sandyleee
6 Set Structures(of(Expressions( 2.8( Topic: Factored form of a quadratic function Given the factored form of a quadratic function, identify the vertex, intercepts, and vertical stretch of the parabola. 11. = = = a.vertex: a.vertex: a.vertex: ))))))b.xlinter(s) b.xlinter(s) b.xlinter(s) c.ylinter c.ylinter: c.ylinter d.stretch d.stretch d.stretch 14. = = = 25 9 a.vertex: a.vertex: a.vertex: ))))))b.xlinter(s) b.xlinter(s) b.xlinter(s) c.ylinter c.ylinter: c.ylinter d.stretch d.stretch d.stretch 17. = = = a.vertex: a.vertex: a.vertex: ))))))b.xlinter(s) b.xlinter(s) b.xlinter(s) c.ylinter c.ylinter: c.ylinter d.stretch d.stretch d.stretch SECONDARY II // MODULE 2
7 52 GO Topic: Vertex form of a quadratic equation Structures(of(Expressions( 2.8( Given the vertex form of a quadratic function, identify the vertex, intercepts, and vertical stretch of the parabola. 20. = = = a.vertex: a.vertex: a.vertex: ))))))b.xlinter(s) b.xlinter(s) b.xlinter(s) c.ylinter c.ylinter: c.ylinter d.stretch d.stretch d.stretch 23. = = = a.vertex: a.vertex: a.vertex: ))))))b.xlinter(s) b.xlinter(s) b.xlinter(s) c.ylinter c.ylinter: c.ylinter d.stretch d.stretch d.stretch 26. Did you notice that the parabolas in problems 11, 12, & 13 are the same as the ones in problems 23, 24, & 25 respectively? If you didn t, go back and compare the answers in problems 11, 12, & 13 and problems 23, 24, & 25. Prove that a = b = c = SECONDARY II // MODULE 2
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