初中数学中考题典函数 学生 15页

初中函数中考汇编（1）一次函数典例1.(★★★)若函数是一次函数，则它的解析式是____________。典例2(★★★)函数.的自变量的取值范围是_________。A.x≥9B.x≠9C.x≥0D.x≥0且x≠9x/小时y/千米600146OFECD（第20题）考点二：一次函数的图像性质及增减性典例3如果点和点是直线上的两点，且当时，，那么函数的图象大致是（）yxOyxOyxOyxOA．B．C．D．4-2考点三：待定系数法求函数关系式典例4已知如图（4-2）直线经过（1，2）和点（3，0），求这条直线的解析式.4-3典例5.如右图（4-3）strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n，已知直线y=-x+2与x轴、y轴分别交于点A、B，另一直线y=kx+b（k≠0）经过点C（1,0），且把⊿ABC分成两部分。（1）若被分成的两部分面积相等，求经过点C的直线解析式；（2）若被分成的两部分面积比为1：5，求经过点C的直线解析式。4-4考点四：实际问题构建一次函数图像典例6.（★★★）小明骑自行车上学，开始以正常速度匀速行驶，途中自行车出了故障，他只好停下来修车，车修好后，因怕耽误上课，故加快速度匀速行驶赶往学校，下图（4-5）是行驶路程s（米）与时间x（分钟）的函数图象那么符合小明骑车行驶情况的图象大致是（）典例7.（2011临沂第14题★★★）甲、乙两同学同时从400m环形跑道上的同一点出犮，同向而行．甲的速度为6m/s，乙的速度为4m/s．设经过x（单位：s）后，跑道上此两人间的较短部分的长度为y（单位：m）．则y与x（0≤x≤300）之间的函数关系可用图象（4-6）表示为（　　）A、B、C、D、4-7考点五：一次函数图像的交点strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n典例8.如图（4-9-1），已知直线与直线相交于点分别交轴于两点．矩形的顶点分别在直线上，顶点都在轴上，且点与点重合．（1）求的面积；（2）求矩形的边与的长；（3）若矩形从原点出发，沿轴的反方向以每秒1个单位长度的速度平移，设移动时间为秒，矩形与重叠部分的面积为，求关于的函数关系式，并写出相应的的取值范围。ADBEOCFxyy（G）（4-9-1）典例9.如图（4-10），已知一次函数y=-x+7与正比例函数y=x的图象交于点A，且与x轴交于点B.（1）求点A和点B的坐标；（2）过点A作AC⊥y轴于点C，过点B作直线l∥y轴．动点P从点O出发，以每秒1个单位长的速度，沿O—C—A的路线向点A运动；同时直线l从点B出发，以相同速度向左平移，在平移过程中，直线l交x轴于点R，交线段BA或线段AO于点Q．当点P到达点A时，点P和直线l都停止运动．在运动过程中，设动点P运动的时间为t秒.①当t为何值时，以A、P、R为顶点的三角形的面积为8？②是否存在以A、P、Q为顶点的三角形是等腰三角形？若存在，求t的值；若不存在，请说明理由．4-10strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n考点六：一次函数的平移典例10.(2010福建泉州市惠安县第12题★★★)将直线向下平移3个单位所得直线的解析式为___________________.考点七：一次函数在实际中的应用典例11.（★★★）某通讯公司推出①、②两种通讯收费方式供用户选择，其中一种有月租费，另一种无月租费，且两种收费方式的通讯时间x（分钟）与收费y（元）之间的函数关系如图所示．（1）有月租费的收费方式是__________（填①或②），月租费是________元；（2）分别求出①、②两种收费方式中y与自变量x之间的函数关系式；（3）请你根据用户通讯时间的多少，给出经济实惠的选择建议．典例12.如图4-15所示，某地区对某种药品的需求量y1（万件），供应量y2（万件）与价格x（元/件）分别近似满足下列函数关系式：y1=－x+70，y2=2x－38，需求量为0时，即停止供应.当y1=y2时，该药品的价格称为稳定价格，需求量称为稳定需求量.（1）求该药品的稳定价格与稳定需求量.（2）价格在什么范围内，该药品的需求量低于供应量？（3）由于该地区突发疫情，政府部门决定对药品供应方提供价格补贴来提高供货价格，以利提高供应量.根据调查统计，需将稳定需求量增加6万件，政府应对每件药品提供多少元补贴，才能使供应量等于需求量.Ox(元/件)y(万件)y1=－x+70y2=2x－384-15初中函数中考汇编（2）反比例函数strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n考点二：反比例函数性质典例2.已知二次函数的图像如图4-20所示，那么一次函数和反比例函数在同一平面直角坐标系中的图像大致是（　　）4-20A．　　B．　　C．　　D．考点三：求反比例函数解析式典例3.如图4-21，过点C（1,2）分别作x轴、y轴的平行线，交直线y=－x+6于A、B两点，若反比例函数（x＞0）的图像与△ABC有公共点，则k的取值范围是（）A．2≤k≤9B.2≤k≤8C.2≤k≤5D.5≤k≤8考点四：反比例函数的实际应用典例4.甲、乙两家商场进行促销活动，甲商场采用“慢200减100”的促销方式，即购买商品的总金额满200元但不足400元，少付100元；满400元但不足600元，少付200元；……，乙商场按顾客购买商品的总金额打6折促销。（1）若顾客在甲商场购买了510元的商品，付款时应付多少钱？（2）若顾客在甲商场购买商品的总金额为x（400≤x＜600）元，优惠后得到商家的优惠率为p（p=），写出p与x之间的函数关系式，并说明p随x的变化情况；（3）品牌、质量、规格等都相同的某种商品，在甲乙两商场的标价都是x（200≤x＜400）元，你认为选择哪家商场购买商品花钱较少？请说明理由。考点六：反比例函数与一次函数的综合应用strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n典例7．如果一次函数与反比例函数的图像相交于点（），那么该直线与双曲线的另一个交点为（）典例8．已知：一次函数y=3x﹣2的图象与某反比例函数的图象的一个公共点的横坐标为1．（1）求该反比例函数的解析式；（2）将一次函数y=3x﹣2的图象向上平移4个单位，求平移后的图象与反比例函数图象的交点坐标；（3）请直接写出一个同时满足如下条件的函数解析式：①函数的图象能由一次函数y=3x﹣2的图象绕点（0，﹣2）旋转一定角度得到；②函数的图象与反比例函数的图象没有公共点．典例9.如图(4-29),已知直线与双曲线交于A，B两点，且点A的横坐标为4.（1）求k的值；（2）若双曲线上一点C的纵坐标为8，求△AOC的面积；（3）过原点O的另一条直线l交双曲线于P，Q两点（P点在第一象限），若由点A，B，P，Q为顶点组成的四边形面积为24，求点P的坐标．4-29strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n考点七：反函数函数和几何图形的综合应用典例10如图4-38，等边△OAB和等边△AFE的一边都在x轴上，双曲线y=（k>0）经过边OB的中点C和AE的中点D，已知等边△OAB的边长为4.（1）求该双曲线所表示的函数解析式；（2）求等边△AEF的边长.4-38典例11.我们容易发现：反比例函数的图象是一个中心对称图形.你可以利用这一结论解决问题。如图4-40，在同一直角坐标系中，正比例函数的图象可以看作是：将轴所在的直线绕着原点逆时针旋转α度角后的图形。若它与反比例函数的图象分别交于第一、三象限的点、，已知点、。（1）直接判断并填写：不论α取何值，四边形的形状一定是;（2）①当点为时，四边形是矩形，试求、α、和有值；②观察猜想：对①中的值，能使四边形为矩形的点共有几个？(不必说理)（3）试探究：能不能是菱形？若能,直接写出B点的坐标,若不能,说明理由。4-40strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n典例12.如图4-42-1，已知正比例函数和反比例函数的图像都经过点M（－2，），且P（-1，－2）为双曲线上的一点，Q为坐标平面上一动点，PA垂直于x轴，QB垂直于y轴，垂足分别是A、B．（1）写出正比例函数和反比例函数的关系式；（2）当点Q在直线MO上运动时，直线MO上是否存在这样的点Q，使得△OBQ与△OAP面积相等？如果存在，请求出点的坐标，如果不存在，请说明理由；（3）如图4-42-2，当点Q在第一象限中的双曲线上运动时，作以OP、OQ为邻边的平行四边形OPCQ，求平行四边形OPCQ周长的最小值．4-42-14-42-2MMstrengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n初中函数中考汇编（3）二次函数考点一、求二次函数的的解析式典例1.（★★★）已知一抛物线的顶点是（1，16），且交与x轴A、B两点（A在B的左边），若∣AB∣=8,求该抛物线的解析式xyO3 －9－1－1AB4-49考点二、二次函数（a≠0）的图像与性质典例2（★★★★）如图4-49，已知二次函数的图像经过点A和点B．（1）求该二次函数的表达式；（2）写出该抛物线的对称轴及顶点坐标；（3）点P（m，m）与点Q均在该函数图像上（其中m＞0），且这两点关于抛物线的对称轴对称，求m的值及点Q到x轴的距离．考点三、二次函数（a≠0）的增减性典例3.（★★★）二次函数（a≠0）的图4-51象如图所示，根据图象解答下列问题：（1）写出方程的两个根．（2分）（2）写出不等式＞0的解集．（2分）（3）写出y随x的增大而减小的自变量x的取值范围．（2分）（4）若方程有两个不相等的实数根，求k的取值范围．（4分）strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n4-51考点四、二次函数（a≠0）最(大或小)值：典例4.如图4-52，抛物线经过A（4,0），B（1,0），C（0，-2）三点．（1）求出抛物线的解析式；（2）P是抛物线上一动点，过P作轴，垂足为M，是否存在P点，使得以A，P，M为顶点的三角形与相似？若存在，请求出符合条件的点P的坐标；若不存在，请说明理由；（3）在直线AC上方的抛物线上有一点D，使得的面积最大，求出点D的坐标．OxyABC414-52考点五、二次函数与一次函数的综合应用典例5、如图4-57：二次函数y=﹣x2+ax+b的图象与x轴交于A（-，0），B（2，0）两点，且与y轴交于点C．（1）求该抛物线的解析式，并判断△ABC的形状；（2）在x轴上方的抛物线上有一点D，且A、C、D、B四点为顶点的四边形是等腰梯形，请直接写出D点的坐标；（3）在此抛物线上是否存在点P，使得以A、C、B、P四点为顶点的四边形是直角梯形？若存在，求出P点的坐标；若不存在，说明理由．ACB4-57strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n典A2例6.阅读材料：如图4-60-1过△ABC的三个顶点分别作出与水平线垂直的三条直线外侧两条直线之间的距离叫△ABC的“水平宽”（a），中间的这条直线在△ABC内部的线段的长度叫△ABC的“铅垂高”（h）我们可行出生种计算三角形面积的新方：，即三角形面积等于水平宽与铅垂高乘积的一半。解答下列问题：如图4-60-2，抛物线顶点坐标为点C(1,4),交x轴于点A(3,0)，交y轴于点B.(1)求抛物线和直线AB的解析式；(2)点P是抛物线(在第一象限内)上的一个动点，连结PA，PB，当P点运动到顶点C时，求△CAB的铅垂高CD及；(3)是否存在一点P，使S△PAB=S△CAB，若存在，求出P点的坐标；若不存在，请说明理由.4-60-2xCOyABD114-60-1典例7.如图4-61，已知二次函数的图象经过三点A（﹣1，0），B（3，0），C（0，3），它的顶点为M，又正比例函数y=kx的图象于二次函数相交于两点D、E，且P是线段DE的中点．（1）求该二次函数的解析式，并求函数顶点M的坐标；（2）已知点E（2，3），且二次函数的函数值大于正比例函数时，试根据函数图象求出符合条件的自变量x的取值范围；（3）0＜k＜2时，求最小值．strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n【参考公式：已知两点D（x1，y1），E（x2，y2），则线段DE的中点坐标为（，）】4-61考点六、二次函数与几何图形的综合应用典例8.矩形在平面直角坐标系中位置如图4-67所示，两点的坐标分别为，，直线与边相交于点．（1）求点的坐标；（2）若抛物线经过点，试确定此抛物线的表达式；（3）设（2）中的抛物线的对称轴与直线交于点，点为对称轴上一动点，以为顶点的三角形与相似，求符合条件的点的坐标．yOCDB6Ax4-67典例9.如图4-69，已知直线过点A（0,1）和B（1,0），P是轴正半轴上的动点，OP的垂直平分线交L于点Q，交x轴于点M．（1）直接写出直线的解析式；（2）设，的面积为，求关于t的函数关系式；并求出当时，的最大值；（3）直线过点且与轴平行，问在上是否存在点，使得是以strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n为直角顶点的等腰直角三角形？若存在，求出点C的坐标，并证明；若不存在，请说明理由．LAOMPBxyL14-69Q典例10．如图4-71-1所示，在平面直角坐标系中，一直抛物线经过A（-4,0），B（0，-4），C（2,0）三点。（1）求抛物线的解析式；（2）若点M为第三象限内抛物线上一动点，点M的横坐标为m，△AMB的面积为S，求S关于m的函数关系式，并求出S的最大值；（3）若点P是抛物线上的动点，点Q是直线y=-x上的动点，判断有几个位置能使以点P、Q、B、O为顶点的四边形为平行四边形，直接写出相应的点的坐标。4-724-71-1典例11.如图4-72，已知平面直角坐标系xoy中，有一矩形纸片OABC，O为坐标原点，AB∥x轴，B（3，），现将纸片按如图折叠，AD，DE为折痕，∠OAD=30度．折叠后，点O落在点O1，点C落在线段AB点C1处，并且DO1与DC1在同一直线上．（1）求折痕AD所在直线的解析式；（2）求经过三点O，C1，C的抛物线的解析式；（3）若⊙P的半径为R，圆心P在（2）的抛物线上运动，⊙P与两坐标轴都相切时，求⊙P半径R的值．典例12.如图所示，已知抛物线的图象与轴相交于点，点在该抛物线图象上，且以为直径的⊙恰好经过顶点.（1）求的值;strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n（2）求点的坐标；（3）若点的纵坐标为，且点在该抛物线的对称轴上运动，试探索：①当时，求的取值范围（其中：为△的面积，为△的面积，为四边形OACB的面积）；②当取何值时，点在⊙上.（写出的值即可）考点七、二次函数的实际应用典例13.已知某种水果的批发单价与批发量的函数关系如图（4-81）所示．（1）请说明图中①、②两段函数图象的实际意义．（2）写出批发该种水果的资金金额w（元）与批发量m（kg）之间的函数关系式；在下图的坐标系中画出该函数图象；指出金额在什么范围内，以同样的资金可以批发到较多数量的该种水果．（3）经调查，某经销商销售该种水果的日最高销量与零售价之间的函数关系如图（2）所示，该经销商拟每日售出60kg以上该种水果，且当日零售价不变，请你帮助该经销商设计进货和销售的方案，使得当日获得的利润最大．4-81典例14.某超市经销一种销售成本为每件40元的商品．据市场调查分析，如果按每件50元销售，一周能售出500件；若销售单价每涨1元，每周销量就减少10件．设销售单价为x元(x≥50)，一周的销售量为y件．(1)写出y与x的函数关系式(标明x的取值范围)；(2)设一周的销售利润为S，写出S与x的函数关系式，并确定当单价在什么范围内变化时，利润随着单价的增大而增大？(3)在超市对该种商品投入不超过10000元的情况下，使得一周销售例如达到8000元，销售单价应定为多少？典例15、某商店经销一种销售成本为每千克40元的水产品，据市场分析，若按每千克50元销售，一个月能售出500千克，销售单价每涨1元，月销售量就减少10千克，针对这种水产品的销售情况，请回答以下问题：（1）当销售单价定为每千克55元时，计算月销售量和月销售利润；（2）设销售单价定为每千克x元，月销售利润为y元，求y与x的函数解析式；（不必写出取值范围）（3）商店想在月销售成本不超过10000元的情况下，使得月销售利润达到8000元，销售单价定为多少？典例16、如图4-83所示，有一座抛物线形拱桥，桥下面在正常水位AB时，宽20米，水位上升3米就达到警戒线CD，这是水面宽度为10米，（1）在如图的坐标系中求出抛物线的解析式；（2）若洪水到来时，水位已0.2米每小时的速度上升，从警戒线开始，在持续多少小时才能到达拱桥顶？strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15\n4-83strengthenthesenseofresponsibility,worktosolvethelackofdecentoccupationexplainaway,conductproblems.Toestablishtheoverallconcept,eliminatedepartmentalism.Strictassessmentandaccountability,tosolvethespiritualslack,nianqingpazhong,statusquo,andotherissues.ToestablishandperfectthemuddlealongBureaustaffconductworkregulations,standardizethebehaviorofpersonnel.2.Tostrengthentheresponsibilitysystem.Oneisthein-depthstudyandimplementthe"HunanprovincialPartyandgovernmentleadingcadresInterimProvisionsontheworksafetyofapairof>(HunanOfficeissued2013No.5),"Hunanprovincesafetysupervisionandmanagementresponsibilitiesoftheprovisionsontheproduction(HunanZhengbanmade2013No.4)Andresolutelyimplementthesafetyproductionofthepartywithresponsibility,apairofresponsibility."Twoisissuedsafetyproductionadministrationandinspectiontopromotetheresponsibilitiesbearsafetyproductionsupervisiondepartmentsstrictlyandeffectivelyassumedresponsibility.Thethreeistoestablishriskselfcorrectionselfreportingsystemforsafetyinproductionenterprises,promotetheenterprisestoimplementthemainresponsibilityforproductionsafetyisintroduced.Fourstrengthenthecountysafetyproductionsupervisionabilityconstructionwork,promotesafeproductionresponsibilitytothegrassroots.3,strictaccountabilityandtargetmanagement.Adheretothe"whoisincharge,whoisresponsibleforthepipeindustrymustbesafe,GuanShengproductionandoperationmustbesafe,pipebusinessmustcontrolsecurity"principle,theimplementationofsafetyTheproductionof"cure."stagnationsupervisionandleadershipresponsiblesystem.Thesafetyproductionofkeytowns,keyenterprisesandkeyproblems,bythetownshipgovernmentandtheDepartmentresponsibleforthestagnationledthelumpsum,totackletough.Tofurtherincreasetheproductionsafetyindexassessment,strictlyimplementthesafetyproductionofthe"onevoteveto"andtherewardsystem,strengthenthesafetyincentiveandrestraintmechanism.(six)theimplementationoftheworkforceisnotstrong.Thedocuments,meeting,longworkarrangement,checkandsupervisetheimplementationofsmall,poorimplementationofthesystem,theworkisnoteffective.Someleadingcadressenseofpurpose,consciousnessofthemassesisnotstrong,theruling"Forthepeople","theinterestsofthemassesnomatter"conceptunderstandingisnotinplace.Thespecificworktreatswiththedeployment,afewleadingcadrescomplainthatworkistoocomplicated,toomuchresponsibility,thepressureistoolarge,toomuchemphasisonthedifficultyofthework,suchasundergroundminestoavoidthedisasterof"sixsystems"constructionandconstructionofmechanicalventilationtofiletheform,forwardingarrangementswork,noin-depthminingenterprisestopromotethespecificwork,theincreaseinthenumberoffiles,buttheeffectisnotgood,notaccordingtotheactualsituationofnoncoalminesinthecounty,toengagein"acrosstheboard",andthequality15