4.1Quadratics A-level考试纯数学P1课件.ppt

Chapter4Quadratics

QuadraticsexpressionCompletedsquareformCompletingthesquarecontents

Quadraticexpressionsyxyxbx+cy=ax2+

Theexpressionax2+bx+c,wherea,bandcareconstants,iscalledaquadraticThenumberbandccanbeanynumbersyouplease,including0,butacannotbe0.Thenumbera,bandcarecalledcoefficients:aisthecoefficientofx2,bisthecoefficientofxandcisoftencalledtheconstantterm.2x2–x+4

Completedsquareformx2–6x+8x2+1x2+2x+3(x–4)(x–2)x2+1x2+2x+3(x–3)2–1x2+1(x+1)2+2

ExampleLocatethevertexandtheaxisofsymmetryofthequadraticgraphy=3–2(x+2)2y=x2–6x+8Solvetheequation3(x–2)2–2=0

Completingthesquarex2–6x+8x2+1x2+2x+1(x–3)2–1x2+1(x+1)2ax2+bx+ca(x+)2–+c

ExampleWritex2+10x+32incompletedsquareformExpress2x2+10x+7incompletedsquareform

ExampleExpress12x2–7x–12incompletedsquareform,anduseyourresulttofindthefactorsof12x2–7x–12Expressx2–8x+12incompletedsquareform.Useyourresulttofindtherangeofthefunctionf(x)=x2–8x+12,whichisdefinedforallrealvaluesofx

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