etad 803 assignment 1 - completing the square

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  • 7/31/2019 ETAD 803 Assignment 1 - Completing the Square

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    Comple'ngthesquareisaprocessthatisusuallycoveredingrade11mathcourses.

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    Thislessonwillfocusonlyonquadra'cswithaleadingcoefficientora-valueof1. Forexample,y=x2+8x-7andnoty=2x2+8x7. Thereisanimportantextrastepinthatprocedurethatisrequiredtohave

    adifferentleadingcoefficient,anditwillnotbecoveredinthisbasic

    introduc'on

    Anexampleofaquadra'cinvertexformisy=(x+3)2+5. Studentswillhavepreviousexperiencegraphingquadra'csinvertexform. Emphasizethebenefitofhavingthequadra'cinvertexformtoallowforeasier

    graphing.

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    Thesestepsareveryspecificandshouldbecompletedinthisorder.

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    Thisstepissome'mesalreadycompletedforyou.Inthosecases,youdonotneedtodoanythinginstep1.

    Besurethatyoury-valueisposi've,ifitisnot,thendividealltermsbynega've1orchangeallofthesignsfrom+to-orviceversa.

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    Simplyplacebracketsaroundthefirsttwoterms. Notthatinthecasewearecoveringhereawillalwaysbeequalto1andwillnot

    bewriPenintheques'on.

    brepresentsanumericalcoefficient.

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    Besuretodothisworktothesideoftheques'onastonotmuddleupthestringofchangestotheoriginalfunc'on.

    Notethatthisvaluewillalwaysendupposi'vebecauseyouaresquaringanumber.

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    Inthisstepweareaddingthisvalueinordertoturntheexpressionwithinthebracketsintoaperfecttrinomialsquare.

    Thisiswhytheprocessiscalledcomple'ngthesquare.

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    ThisstepiseasilyforgoPen. Stresstheimportanceofthisstepbymakingitveryclearthattheequa'on

    cannotbechangedandmustremainbalanced.

    Byaddingandthensubtrac'ngthesamevalue,wearenotchangingtheequa'onbecauseweareaddingzero(e.g.+4-4=0).

    Addingzerodoesnotchangetheequa'on. Ifweforgettosubtractthisvalue,thenweareinfactchangingthe

    equa'on.

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    Inthisstep,weareusingourpreviousknowledgeoffactoringtofactortheperfecttrinomialsquarewithinthebrackets.

    Ifthepreviousstepshavebeencompletedcorrectly,thenthefactoringshouldalwaysworkouttobethesamebinomialtwice.

    Anothertricktothisfactoringisthatthenumberisalwaysgoingtobeb2. Donotteachthisdirectly,butratherallowthestudentstodiscoverthe

    paPernontheirown.

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    Inthisstepyoujustaddthetermsoutsidethebrackettogether. Rememberthatthefirsttermisanega've.

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    Thisstepisheretoremindstudentsofthereasonforcomple'ngthesquare. Vertexformisverygoodforgraphing.

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  • 7/31/2019 ETAD 803 Assignment 1 - Completing the Square

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    Thisisjustasummaryofthestepswithadifferentexampleshown.

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  • 7/31/2019 ETAD 803 Assignment 1 - Completing the Square

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    Thisisjustasummaryofthestepswithadifferentexampleshown.

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    Concludebyremindingstudentswhywewanttobeabletocompletethesquare:itistomakegraphingeasy!

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