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1、9780199602124_109_133_CH04.qxd10/7/118:53Page109Chapter4QuadraticequationsOBJECTIVESHavingcompletedthischapteryoushouldbeableto:■Recognizeaquadraticexpression,understandhowitarisesandhowtofactorizeit.■Solveaquadraticexpressionusingtrial-and-errormethods
2、andalsobyusingtheformula.■Understandwhysomequadraticexpressionscannotbefactorizedandwhysomehaveasinglerepeatedfactor.■Recognizeaquadraticfunctionandsketchitsgraph.■Understandtherelationshipbetweenthealgebraicandgraphicalsolutionofaquadraticequation.■Rec
3、ognizeandsolvesimultaneousquadraticequations.■Recognizeandunderstandtheroleofquadraticfunctionsinsupplyanddemandmodelsandastotalcostortotalrevenuefunctions.4.1IntroductionInthepreviouschapterweexaminedlinearequationsandfunctions.Wesawthatalinearequation
4、hasthegeneralformax+b=c,wherexisthevariableorunknownanda,b,andcareconstantsorparameters.Thisequationissaidtobelinearbecausexisraisedonlytothepower1,andtonohigherorlowerpower.Alinearfunctionhasthegeneralformy=ax+bandspecifiesarelationshipbetweenthetwovari
5、ablesorunknowns,xandy.Thisfunctionislinear,inthiscasebecausexandyarebothraisedonlytothepower1,andtonohigherorlowerpower.Wealsosawthatthegraphofthefunctiony=ax+bisastraightline,whichgivesaconcretemeaningtotheterm‘linear’.Aswesawinthepreviouschapter,theke
6、yfeatureofalinearrelationshipbetweentwovari-ablesxandyisthattheslopeofthegraphisconstant,meaningthata1-unitincreaseinxalwaysincreasesordecreasesybythesameamount.Whilesomerelationshipsineconomicsmaybeofthissimplelineartype,obviouslyweneedtodeveloptheabil
7、itytohandlenon-linearrelation-shipstoo,whereagivenchangeinxdoesnotalwayshavethesameeffectony.Inthischapter9780199602124_109_133_CH04.qxd10/7/118:53Page110110wewillexaminequadraticequationsandquadraticfunctions,whicharethesimplesttypeofnon-linearrelation
8、ship.Wewillshowthataquadraticfunction,whengraphed,producesacharacteristicallyU-shapedcurve.Wewillshowhowtosolvequadraticequations,includingsimultaneousquadraticequations.Attheendofthechapterwelookbrieflyattwoapplicationsofquadrati
