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我(奥辞)一(驰颈)般(叠补苍)早(窜补辞)上(厂丑补苍驳)6:30就(闯颈耻)起(蚕颈)床(颁丑耻补苍驳)了(尝颈补辞),这(窜丑别)个(骋别)起(蚕颈)床(颁丑耻补苍驳)时(厂丑颈)间(闯颈补苍)其(蚕颈)实(厂丑颈)和(贬别)上(厂丑补苍驳)班(叠补苍)的(顿别)时(厂丑颈)候(贬辞耻)是(厂丑颈)差(颁丑补)不(叠耻)多(顿耻辞)的(顿别),多(顿耻辞)年(狈颈补苍)的(顿别)生(厂丑别苍驳)物(奥耻)钟(窜丑辞苍驳)养(驰补苍驳)成(颁丑别苍驳)的(顿别)习(齿颈)惯(骋耻补苍),睡(厂丑耻颈)醒(齿颈苍驳)了(尝颈补辞)之(窜丑颈)后(贬辞耻)硬(驰颈苍驳)躺(罢补苍驳)在(窜补颈)床(颁丑耻补苍驳)上(厂丑补苍驳)也(驰别)实(厂丑颈)在(窜补颈)是(厂丑颈)躺(罢补苍驳)不(叠耻)住(窜丑耻),与(驰耻)其(蚕颈)这(窜丑别)样(驰补苍驳),倒(顿补辞)不(叠耻)如(搁耻)起(蚕颈)来(尝补颈)收(厂丑辞耻)拾(厂丑颈)一(驰颈)下(齿颈补)了(尝颈补辞)。一(驰颈)般(叠补苍)就(闯颈耻)是(厂丑颈)起(蚕颈)来(尝补颈)自(窜颈)己(闯颈)洗(齿颈)漱(厂丑耻),然(搁补苍)后(贬辞耻)准(窜丑耻苍)备(叠别颈)做(窜耻辞)早(窜补辞)饭(贵补苍)。
测颈苍飞别颈办别丑耻迟辞耻蝉耻锄补颈锄丑别产颈濒惫诲别迟颈补苍箩颈补苍,肠补颈测耻补苍谤耻丑耻补,辞耻测辞耻测颈锄丑别苍飞别颈蹿别苍驳肠丑耻颈驳耻辞,箩颈补锄补锄丑耻辞迟颈补苍测别辩颈苍驳虫颈苍诲别辩颈虫颈诲补颈锄辞耻濒颈补辞虫颈补谤颈诲别测补苍谤别。谤补苍别谤,锄丑别苍驳蝉丑颈锄丑别测补苍驳测颈驳别苍颈苍驳箩颈苍驳诲别谤颈锄颈,辫颈苍驳箩颈苍驳诲别肠补颈诲颈辩耻别迟耻谤补苍虫颈补苍辩颈濒颈补辞测颈蹿补苍产耻虫颈补辞诲别产辞濒补苍。测颈迟颈补辞虫颈辩颈驳耻驳耻补颈诲别驳耻补颈蝉丑别辩颈补辞谤补苍虫颈补苍蝉丑别苍,谤补苍驳辫颈苍驳谤颈濒颈丑补苍丑辞耻辫耻蝉丑颈诲别濒补辞锄丑补苍驳蝉丑辞耻尘补苍驳箩颈补辞濒耻补苍,锄丑别苍办别飞别颈“蝉丑别肠丑耻尘别颈,濒补辞锄丑补苍驳箩颈苍驳箩颈补辞”。
初(Chu)三(San)数(Shu)学(Xue)知(Zhi)识(Shi)点(Dian)整(Zheng)理(Li)(九(Jiu)上(Shang) § 22.1二(Er)次(Ci)函(Han)数(Shu)一(Yi)般(Ban)式(Shi)的(De)图(Tu)像(Xiang)与(Yu)性(Xing)质(Zhi))原(Yuan)创(Chuang)2023-06-01 00:50·泛(Fan)海(Hai)学(Xue)舟(Zhou)第(Di)二(Er)十(Shi)二(Er)章(Zhang) 二(Er)次(Ci)函(Han)数(Shu)第(Di)三(San)节(Jie) 二(Er)次(Ci)函(Han)数(Shu)y=ax2+bx+c(a≠0)的(De)图(Tu)象(Xiang)与(Yu)性(Xing)质(Zhi)【学(Xue)习(Xi)目(Mu)标(Biao)】1. 会(Hui)用(Yong)描(Miao)点(Dian)法(Fa)画(Hua)二(Er)次(Ci)函(Han)数(Shu)的(De)图(Tu)象(Xiang);会(Hui)用(Yong)配(Pei)方(Fang)法(Fa)将(Jiang)二(Er)次(Ci)函(Han)数(Shu)的(De)解(Jie)析(Xi)式(Shi)写(Xie)成(Cheng)的(De)形(Xing)式(Shi);2.通(Tong)过(Guo)图(Tu)象(Xiang)能(Neng)熟(Shu)练(Lian)地(Di)掌(Zhang)握(Wo)二(Er)次(Ci)函(Han)数(Shu)的(De)性(Xing)质(Zhi);3.经(Jing)历(Li)探(Tan)索(Suo)与(Yu)的(De)图(Tu)象(Xiang)及(Ji)性(Xing)质(Zhi)紧(Jin)密(Mi)联(Lian)系(Xi)的(De)过(Guo)程(Cheng),能(Neng)运(Yun)用(Yong)二(Er)次(Ci)函(Han)数(Shu)的(De)图(Tu)象(Xiang)和(He)性(Xing)质(Zhi)解(Jie)决(Jue)简(Jian)单(Dan)的(De)实(Shi)际(Ji)问(Wen)题(Ti),深(Shen)刻(Ke)理(Li)解(Jie)数(Shu)学(Xue)建(Jian)模(Mo)思(Si)想(Xiang)以(Yi)及(Ji)数(Shu)形(Xing)结(Jie)合(He)的(De)思(Si)想(Xiang).【要(Yao)点(Dian)梳(Shu)理(Li)】要(Yao)点(Dian)一(Yi)、二(Er)次(Ci)函(Han)数(Shu)与(Yu)之(Zhi)间(Jian)的(De)相(Xiang)互(Hu)关(Guan)系(Xi)1.顶(Ding)点(Dian)式(Shi)化(Hua)成(Cheng)一(Yi)般(Ban)式(Shi)从(Cong)函(Han)数(Shu)解(Jie)析(Xi)式(Shi)我(Wo)们(Men)可(Ke)以(Yi)直(Zhi)接(Jie)得(De)到(Dao)抛(Pao)物(Wu)线(Xian)的(De)顶(Ding)点(Dian)(h,k),所(Suo)以(Yi)我(Wo)们(Men)称(Cheng)为(Wei)顶(Ding)点(Dian)式(Shi),将(Jiang)顶(Ding)点(Dian)式(Shi)去(Qu)括(Kuo)号(Hao),合(He)并(Bing)同(Tong)类(Lei)项(Xiang)就(Jiu)可(Ke)化(Hua)成(Cheng)一(Yi)般(Ban)式(Shi).2.一(Yi)般(Ban)式(Shi)化(Hua)成(Cheng)顶(Ding)点(Dian)。要(Yao)点(Dian)诠(Zuo)释(Shi):1.抛(Pao)物(Wu)线(Xian)的(De)对(Dui)称(Cheng)轴(Zhou)是(Shi)直(Zhi)线(Xian),顶(Ding)点(Dian)坐(Zuo)标(Biao)是(Shi),可(Ke)以(Yi)当(Dang)作(Zuo)公(Gong)式(Shi)加(Jia)以(Yi)记(Ji)忆(Yi)和(He)运(Yun)用(Yong).2.求(Qiu)抛(Pao)物(Wu)线(Xian)的(De)对(Dui)称(Cheng)轴(Zhou)和(He)顶(Ding)点(Dian)坐(Zuo)标(Biao)通(Tong)常(Chang)用(Yong)三(San)种(Zhong)方(Fang)法(Fa):配(Pei)方(Fang)法(Fa)、公(Gong)式(Shi)法(Fa)、代(Dai)入(Ru)法(Fa),这(Zhe)三(San)种(Zhong)方(Fang)法(Fa)都(Du)有(You)各(Ge)自(Zi)的(De)优(You)缺(Que)点(Dian),应(Ying)根(Gen)据(Ju)实(Shi)际(Ji)灵(Ling)活(Huo)选(Xuan)择(Ze)和(He)运(Yun)用(Yong).要(Yao)点(Dian)二(Er)、二(Er)次(Ci)函(Han)数(Shu)的(De)图(Tu)象(Xiang)的(De)画(Hua)法(Fa)1.一(Yi)般(Ban)方(Fang)法(Fa):列(Lie)表(Biao)、描(Miao)点(Dian)、连(Lian)线(Xian);2.简(Jian)易(Yi)画(Hua)法(Fa):五(Wu)点(Dian)定(Ding)形(Xing)法(Fa).其(Qi)步(Bu)骤(Zhou)为(Wei):(1)先(Xian)根(Gen)据(Ju)函(Han)数(Shu)解(Jie)析(Xi)式(Shi),求(Qiu)出(Chu)顶(Ding)点(Dian)坐(Zuo)标(Biao)和(He)对(Dui)称(Cheng)轴(Zhou),在(Zai)直(Zhi)角(Jiao)坐(Zuo)标(Biao)系(Xi)中(Zhong)描(Miao)出(Chu)顶(Ding)点(Dian)M,并(Bing)用(Yong)虚(Xu)线(Xian)画(Hua)出(Chu)对(Dui)称(Cheng)轴(Zhou).(2)求(Qiu)抛(Pao)物(Wu)线(Xian)与(Yu)坐(Zuo)标(Biao)轴(Zhou)的(De)交(Jiao)点(Dian),当(Dang)抛(Pao)物(Wu)线(Xian)与(Yu)x轴(Zhou)有(You)两(Liang)个(Ge)交(Jiao)点(Dian)时(Shi),描(Miao)出(Chu)这(Zhe)两(Liang)个(Ge)交(Jiao)点(Dian)A、B及(Ji)抛(Pao)物(Wu)线(Xian)与(Yu)y轴(Zhou)的(De)交(Jiao)点(Dian)C,再(Zai)找(Zhao)到(Dao)点(Dian)C关(Guan)于(Yu)对(Dui)称(Cheng)轴(Zhou)的(De)对(Dui)称(Cheng)点(Dian)D,将(Jiang)A、B、C、D及(Ji)M这(Zhe)五(Wu)个(Ge)点(Dian)按(An)从(Cong)左(Zuo)到(Dao)右(You)的(De)顺(Shun)序(Xu)用(Yong)平(Ping)滑(Hua)曲(Qu)线(Xian)连(Lian)结(Jie)起(Qi)来(Lai).要(Yao)点(Dian)诠(Zuo)释(Shi):当(Dang)抛(Pao)物(Wu)线(Xian)与(Yu)x轴(Zhou)只(Zhi)有(You)一(Yi)个(Ge)交(Jiao)点(Dian)或(Huo)无(Wu)交(Jiao)点(Dian)时(Shi),描(Miao)出(Chu)抛(Pao)物(Wu)线(Xian)与(Yu)y轴(Zhou)的(De)交(Jiao)点(Dian)C及(Ji)对(Dui)称(Cheng)点(Dian)D,由(You)C、M、D三(San)点(Dian)可(Ke)粗(Cu)略(Lue)地(Di)画(Hua)出(Chu)二(Er)次(Ci)函(Han)数(Shu)图(Tu)象(Xiang)的(De)草(Cao)图(Tu);如(Ru)果(Guo)需(Xu)要(Yao)画(Hua)出(Chu)比(Bi)较(Jiao)精(Jing)确(Que)的(De)图(Tu)象(Xiang),可(Ke)再(Zai)描(Miao)出(Chu)一(Yi)对(Dui)对(Dui)称(Cheng)点(Dian)A、B,然(Ran)后(Hou)顺(Shun)次(Ci)用(Yong)平(Ping)滑(Hua)曲(Qu)线(Xian)连(Lian)结(Jie)五(Wu)点(Dian),画(Hua)出(Chu)二(Er)次(Ci)函(Han)数(Shu)的(De)图(Tu)象(Xiang),要(Yao)点(Dian)三(San)、二(Er)次(Ci)函(Han)数(Shu)的(De)图(Tu)象(Xiang)与(Yu)性(Xing)质(Zhi)1.二(Er)次(Ci)函(Han)数(Shu)图(Tu)象(Xiang)与(Yu)性(Xing)质(Zhi)函(Han)数(Shu) 二(Er)次(Ci)函(Han)数(Shu)(a、b、c为(Wei)常(Chang)数(Shu),a≠0)增(Zeng)减(Jian)性(Xing) 在(Zai)对(Dui)称(Cheng)轴(Zhou)的(De)左(Zuo)侧(Ce),即(Ji)当(Dang)时(Shi),y随(Sui)x的(De)增(Zeng)大(Da)而(Er)减(Jian)小(Xiao);在(Zai)对(Dui)称(Cheng)轴(Zhou)的(De)右(You)侧(Ce),即(Ji)当(Dang)时(Shi),y随(Sui)x的(De)增(Zeng)大(Da)而(Er)增(Zeng)大(Da).简(Jian)记(Ji):左(Zuo)减(Jian)右(You)增(Zeng) 在(Zai)对(Dui)称(Cheng)轴(Zhou)的(De)左(Zuo)侧(Ce),即(Ji)当(Dang)时(Shi),y随(Sui)x的(De)增(Zeng)大(Da)而(Er)增(Zeng)大(Da);在(Zai)对(Dui)称(Cheng)轴(Zhou)的(De)右(You)侧(Ce),即(Ji)当(Dang)时(Shi),y随(Sui)x的(De)增(Zeng)大(Da)而(Er)减(Jian)小(Xiao).简(Jian)记(Ji):左(Zuo)增(Zeng)右(You)减(Jian)。最(Zui)大(Da)(小(Xiao))值(Zhi) 抛(Pao)物(Wu)线(Xian)有(You)最(Zui)低(Di)点(Dian),当(Dang)时(Shi),y有(You)最(Zui)小(Xiao)值(Zhi), 抛(Pao)物(Wu)线(Xian)有(You)最(Zui)高(Gao)点(Dian),当(Dang)时(Shi),y有(You)最(Zui)大(Da)值(Zhi),2.二(Er)次(Ci)函(Han)数(Shu)图(Tu)象(Xiang)的(De)特(Te)征(Zheng)与(Yu)a、b、c及(Ji)b2-4ac的(De)符(Fu)号(Hao)之(Zhi)间(Jian)的(De)关(Guan)系(Xi)字(Zi)母(Mu) 字(Zi)母(Mu)的(De)符(Fu)号(Hao) 图(Tu)象(Xiang)的(De)特(Te)征(Zheng)a a>0 开(Kai)口(Kou)向(Xiang)上(Shang)a<0 开(Kai)口(Kou)向(Xiang)下(Xia)b ab>0(a,b同(Tong)号(Hao)) 对(Dui)称(Cheng)轴(Zhou)在(Zai)y轴(Zhou)左(Zuo)侧(Ce)ab<0(a,b异(Yi)号(Hao)) 对(Dui)称(Cheng)轴(Zhou)在(Zai)y轴(Zhou)右(You)侧(Ce)c c=0 图(Tu)象(Xiang)过(Guo)原(Yuan)点(Dian)c>0 与(Yu)y轴(Zhou)正(Zheng)半(Ban)轴(Zhou)相(Xiang)交(Jiao)c<0 与(Yu)y轴(Zhou)负(Fu)半(Ban)轴(Zhou)相(Xiang)交(Jiao)b2-4ac b2-4ac=0 与(Yu)x轴(Zhou)有(You)唯(Wei)一(Yi)交(Jiao)点(Dian)b2-4ac>0 与(Yu)x轴(Zhou)有(You)两(Liang)个(Ge)交(Jiao)点(Dian)b2-4ac<0 与(Yu)x轴(Zhou)没(Mei)有(You)交(Jiao)点(Dian)要(Yao)点(Dian)四(Si)、求(Qiu)二(Er)次(Ci)函(Han)数(Shu)的(De)最(Zui)大(Da)(小(Xiao))值(Zhi)的(De)方(Fang)法(Fa)如(Ru)果(Guo)自(Zi)变(Bian)量(Liang)的(De)取(Qu)值(Zhi)范(Fan)围(Wei)是(Shi)全(Quan)体(Ti)实(Shi)数(Shu),那(Na)么(Me)函(Han)数(Shu)在(Zai)顶(Ding)点(Dian)处(Chu)取(Qu)得(De)最(Zui)大(Da)(或(Huo)最(Zui)小(Xiao))值(Zhi),即(Ji)当(Dang)时(Shi),.要(Yao)点(Dian)诠(Zuo)释(Shi):如(Ru)果(Guo)自(Zi)变(Bian)量(Liang)的(De)取(Qu)值(Zhi)范(Fan)围(Wei)是(Shi)x1≤x≤x2,那(Na)么(Me)首(Shou)先(Xian)要(Yao)看(Kan)是(Shi)否(Fou)在(Zai)自(Zi)变(Bian)量(Liang)的(De)取(Qu)值(Zhi)范(Fan)围(Wei)x1≤x≤x2内(Nei),若(Ruo)在(Zai)此(Ci)范(Fan)围(Wei)内(Nei),则(Ze)当(Dang)时(Shi),,若(Ruo)不(Bu)在(Zai)此(Ci)范(Fan)围(Wei)内(Nei),则(Ze)需(Xu)要(Yao)考(Kao)虑(Lv)函(Han)数(Shu)在(Zai)x1≤x≤x2范(Fan)围(Wei)内(Nei)的(De)增(Zeng)减(Jian)性(Xing),如(Ru)果(Guo)在(Zai)此(Ci)范(Fan)围(Wei)内(Nei),y随(Sui)x的(De)增(Zeng)大(Da)而(Er)增(Zeng)大(Da),则(Ze)当(Dang)x=x2时(Shi),;当(Dang)x=x1时(Shi),,如(Ru)果(Guo)在(Zai)此(Ci)范(Fan)围(Wei)内(Nei),y随(Sui)x的(De)增(Zeng)大(Da)而(Er)减(Jian)小(Xiao),则(Ze)当(Dang)x=x1时(Shi),;当(Dang)x=x2时(Shi),,如(Ru)果(Guo)在(Zai)此(Ci)范(Fan)围(Wei)内(Nei),y值(Zhi)有(You)增(Zeng)有(You)减(Jian),则(Ze)需(Xu)考(Kao)察(Cha)x=x1,x=x2,时(Shi)y值(Zhi)的(De)情(Qing)况(Kuang).
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