抛物线顶点坐标公式及推导

顶点公式啊a(x+b/2a)^2+c-b^2/4a=0

横坐标：-b/2a 纵坐标(4ac-b^2)/4ac

1、公式中的(h，k)为抛物线的顶点，抛物线的顶点式为y=a(x-h)2+k(a≠0)。 2、顶点坐标：对于二次函数y=ax2+bx+c（a≠0）其顶点坐标为 [-b/2a,（4ac-b2）/4a] 3、知道抛物线的顶点,只需再给另一点的坐标就可以求解析式。 4、例如：已知抛物线的顶点为（-3，2）和（2.1）。可设解析式为y=a（x+3）2+2。再把x=2，y=1代入。求得a=-1/25即y=-1/25（x+3）2+2即可。

y=1-x^2y"=-2xy"=0-2x=0x=0x=0, y=1顶点 =（0,1)

抛物线公式:一般式:y=ax2+bx+c(a、b、c为常数，a≠0）顶点式:y=a(x-h）2+k（a、h、k为常数，a≠0）交点式（两根式）：y=a（x-x1）（x-x2）（a≠0）其中是抛物线y=ax2+bx+c(a、b、c为常数，a≠0）与x轴交点坐标，即方程ax2+bx+c=0的两实数根。

不用计算，直接代入顶点坐标公式即可

设：y=ax^2+bx+c y = ax^2+bx+c = a(x+b/2a)^2 + (c-b^2/4a) 故：顶点坐标 x=-b/2a 当 a>0 时,a(x+b/2a)^2≥0 ,y最小值：(c-b^2/4a) 当 a

1、公式中的(h，k)为抛物线的顶点，抛物线的顶点式为y=a(x-h)2+k(a≠0)。 2、顶点坐标：对于二次函数y=ax2+bx+c（a≠0）其顶点坐标为 [-b/2a,（4ac-b2）/4a] 3、知道抛物线的顶点,只需再给另一点的坐标就可以求解析式。 4、例如：已知抛物线的顶点为（-3，2）和（2.1）。可设解析式为y=a（x+3）2+2。再把x=2，y=1代入。求得a=-1/25即y=-1/25（x+3）2+2即可。

答： 对于抛物线f(x)=ax^2+bx+c 推导过程如下： f(x)=ax^2+bx+c =a[x^2+bx/a+b^2/(4a^2)]+c-b^2/(4a) =a(x+b/a)^2+c-b^2/(4a) 当x+b/a=0时,取得最值c-b^2/(4a) 所以：顶点坐标公式为（-b/a,c-b^2/(4a))

可以

用公式法求抛物线的顶点

抛物线是:y=ax^2+bx+c通过配方得:y=a(x^2+b/ax+b^2/(4a^2))+c-b^2/(4a)=a(x+b/2a)^2+(4ac-b^2)/(4a)所以,顶点坐标是:(-b/2a,(4ac-b^2)/4a)对称轴是:x=-b/2a

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是负的吧欸

二次函数顶点坐标公式推导：一般式：y=ax^2+bx+c（baia、b、c为常数，a≠0）顶点式：y=a(x-h)^2+k，抛物线的顶点P（h、k）。对称轴与二次函数图像唯一的交点为二次函数图像的顶点P。当b=0时，二次函数图像的对称轴是y轴（即直线x=0）。是顶点的横坐标（即x=？）。扩展资料：二次项系数a决定抛物线的开口方向和大小。当a>0时，抛物线开口向上；当a<0时，抛物线开口向下；|a|越小，则抛物线的开口越大；|a|越大，则抛物线的开口越小。一次项系数b和二次项系数a共同决定对称轴的位置。当a与b同号时（即ab>0），对称轴在y轴左侧；当a与b异号时（即ab（可巧记为：左同右异）。常数项c决定抛物线与y轴交点。抛物线与y轴交于(0, c）。参考资料来源：百度百科-二次函数

设y=ax^2+bx+c （1）顶点坐标为（-b/2a , c-b^2/4a）因此-b/2a = 6 （2）c-b^2/4a = 180 （3）其他点坐标带入（1）式可得c=150解（2）（3）可得a = -5/6 b=10所以y = -5/6x^2+10x+150

解a＝1＞0，故二次函数开口向上，y＝x2+2x-3＝(x+1)^2-4故顶点为(-1，-4).

一般式：y=ax^2+bx+c（a，b，c为常数，a≠0） 顶点式：y=a(x-h)^2+k [抛物线的顶点P（h，k）] 对于二次函数y=ax^2+bx+c 其顶点坐标为 (-b/2a,(4ac-b^2)/4a)交点式：y=a(x-x69)(x-x 60) [仅限于与x轴有交点A（x69 ，0）和 B（x60，0）的抛物线] 其中x1，2= -b±√b^2－4ac

图都没有一个。

∵抛物线的焦点是F(1,-1),准线方程是x-y=0,∴对称轴为y=-x,且过焦点且与准线垂直的线段的中点处即为顶点,∵过焦点(1,-1),且与准线垂直的垂足为(0,0)∴根据中点坐标公式得抛物线的顶点坐标是(12,-12)故答案为(12,-12).

（1）抛物线顶点为（0,-1），对应抛物线顶点坐标公式（-b/2a,(4ac-b^2)/4a）可得b=0,c=-1；则抛物线解析式：y=x^2-1（2）由第1问求得的解析式可知交于x轴的两点为A（1,0），B（-1,0），由此可得：AB=2，AM=√2，BM=√2，因此AM^2+BM^2=AB^2，且AM=BM，因此△MAB是等腰直角三角形（3）设y=kx，与y=x^2-1联立求解得x=[k+√（k^2+4）]/2或x=[k-√（k^2+4）]/2，把MC和MD的斜率表示出来，MC斜率m=，MD斜率为n=，判断垂直看两直线斜率乘积是否等于-1，斜率求解简单，但此题目表示过于复杂，略我经过计算得m*n=-1，所以两直线垂直

(2a/b,4a/4ac-b^2)a>0,图像开口向下a<0，图像开口向下

顶点坐标公式如果y=ax2+bx+c则顶点坐标为（-b/2a，(4ac-b2)/4a）由此可知顶点坐标为（0，1)

楼主确认是“使QB-QA”？！应该是QB=QA吧？如果是的话，此题可解。由于解题过程书写起来比较麻烦，这里给楼主讲讲解题思路吧。1、由抛物线顶点坐标公式，得到P点坐标；2、由直线的两点式，得到OP的方程；3、联立直线OP与抛物线，得到B点坐标；4、在抛物线方程中，令x=0，得到A点坐标；5、思路：因为QA=QB，所以Q点在AB的中垂线上；6、由直线的两点式，得到AB的方程，从而得到直线AB的斜率；7、由AB斜率，得到AB中垂线的斜率；8、由中点坐标公式，得到AB中点的坐标；9、由直线的点斜式，得到AB中垂线的方程；10、Q点在AB中垂线上，从而得到Q点坐标。有了上述明确的思路、步骤，相信楼主一定能顺利圆满的解决此问题。祝楼主好运。

已知顶点坐标为(k，h)，则设该抛物线的解析式为y=a(x-k)^2+h，(其中a不等于0)，必须再知道一个异于顶点的坐标，然后代入抛物线解析式，从而得出a，然后就求出抛物线解析式了。

楼上抄的对

88kk66.online 这么

There are many factors that account for the phenomenon.

man-made factors

看一下输入法中的软键盘是否有这个符号。办公软件中，可以插入符号的方式。

破折号用以表示思想上突然的中断或转移. －among other factors－表示思想的转移 如：I believed she was wise －well,she was I suppose－in a way.

有影响的英文短语对...有影响的英文短语是haveaneffecton和haveanimpacton。例句如下：1、Societybeginstohaveanimpactonthedevelopingchild.翻译：社会开始对成长中的孩子产生影响。2、Thatwillhaveaneffectonconsumerspendingmoregenerally.翻译：这将对经常消费的消费者产生一定的影响。effect的用法1、effect作“结果，影响”“感受，印象”等解时，既可用作可数名词，也可用作不可数名词；作“个人财产，财物”解时常用复数形式。2、effect常与have，take，come〔go〕into等动词或动词短语连用。3、foreffect通常表示“为了外表好看，为了做样子”；ineffect的意思是“有效”“事实上”；intoeffect的意思是“实施〔行〕”；tonoeffect的意思是“无效”；tothat〔the〕sameeffect的意思是“大意相同〔如此〕”；totheeffectthat...的意思是“其大意是”或“以便”。对有影响短语difference对···有影响的英文：makeadifferencedifference读法?英[?d?fr?ns]??美[?d?fr?ns]n.差别;差异;不同;变化;差;差额;意见分歧;不和短语：1、pricedifference?价格差别2、potentialdifference?n.势差，位差3、makethedifference?有影响，很重要；产生差别4、culturaldifference?文化差异5、essentialdifference?本质区别扩展资料词语用法：1、difference作“差异,区别”解时,指一事物区别于另一事物的不同之处,可指事物之间的本质差别,也可指事物之间的非本质的差别,可充当不可数名词,也可作可数名词。difference还可作“差距,差额”解,指的是事物之间存在的一个差额值,作不可数名词。difference引申还可作“分歧,争执”解,这时常用作复数形式。2、difference后常接介词between,of短语作定语。词义辨析：difference,distinction,discrepancy这组词都有“差别，区别”的意思，其区别是：1、difference?普通用词，可指事物本质上的差异或数量上的差额，也可指事物在某一方面的差别，还可指人们之间的不同意见。2、distinction?较正式用词，除指事物在本质上的差别外，还指在某一方面或某一细节上的区分，要在认真观察、研究后才易觉察。3、discrepancy?多用于言论和记述方面，指两物之间缺乏使之相似或平衡的协调。对某人有影响英文influence对什么有影响的英文：influenceon、effecton一、influenceon英[?influ?ns?n]??美[??nflu?nsɑn]对有影响She"s?not?a?very?good?influence?on?the?youth?of?this?country.她对这个国家的青年一代没什么好影响。二、effecton英[i?fekt?n]??美[??f?ktɑn]对有影响1、The?illness?had?a?profound?effect?on?his?outlook这场病对他的人生观产生了深刻的影响。2、His?visit?had?a?great?effect?on?them.他的来访对他们产生了巨大影响。扩展资料近义词：一、makeadifference、impacton英[meik??dif?r?ns]??美[meke?d?f?r?ns]有影响;起作用Your?support?will?certainly?make?a?difference?in?my?cause.你的支持肯定对我的事业很有影响。二、impacton英[?imp?kt?n]??美[??m?p?ktɑn]对冲击，碰撞，影响Society?begins?to?have?an?impact?on?the?developing?child.社会开始对成长中的孩子产生影响。对某人有很大的影响短语英语短语haveaneffecton和haveanimpacton都可以表示对．．．有重大的影响。haveainfluenceon多指潜移默化的影响，类似＂近朱者赤＂，比如父母对儿女的影响等等，haveaneffecton则多指事物变化产生的后果，有时间因果的先后，倾向于＂效果＂的意思。例句：1、TheInternethasanimpactonoureverydaylives.互联网对我们的日常生活有着重大的影响。2、Thereisnodoubtthatmoneyhasanimpactonourhappiness.毫无疑问，金钱对我们的幸福有很大的影响。3、Herspeechmadeaprofoundimpactoneveryone.她的讲话对每个人都有深远的影响。扩展资料effect英美n.效应；影响；结果；外观，声响，印象，效果；财产，所有物，财物v.使发生；实现；引起第三人称单数：effects复数：effects现在分词：effecting过去式：effected过去分词：effected例句：Thecrisishadanegativeeffectontrade.这次危机对贸易产生了很坏的影响。对...有影响的英文短语influence一、effecton?sth英[i?fekt?n]??美[??f?ktɑn]对有影响The?illness?had?a?profound?effect?on?his?outlook这场病对他的人生观产生了深刻的影响。二、haveeffecton?sth英[h?vi?fekt?n]??美[h?v??f?ktɑn]对有影响The?factors?that?have?effect?on?the?DEG?content?in?PET?chip?were?discussed.讨论了影响切片中二甘醇含量的各种因素。三、haveanimpacton?sth英[h?v?n?imp?kt?n]??美[h?v?n??m?p?ktɑn]对有影响，对起作用，产生效果Society?begins?to?have?an?impact?on?the?developing?child.社会开始对成长中的孩子产生影响。四、influenceon?sth英[?influ?ns?n]??美[??nflu?nsɑn]对有影响It?exerts?a?civilizing?influence?on?mankind.这产生了教化人类的影响。五、haveabearingonsth英[h?v??b??ri??n]??美[h?ve?b?r??ɑn]关系到，影响到;有关Exposuretoemergingmarketscouldhaveabearingonwhatstocksprovetobedefensive.对新兴市场的投资可能影响到那些股票才算防御性股票。

contributing factors 成因Because most of these deaths are classified as suicides regardless of additional or contributing factors, thesoldiers" families find it difficult to collect survivors" benefits. 由于大多数军人死亡事件无论有无其他因素或促成因素，都被定为自杀，致使军人家属难以领取抚恤金。

电脑上打“：”帽号的几种方法：所需材料：QQ输入法。一、第一种方法：也是最简单的方法，在任意一种输入法下按下组合键Ctrl+；即可输入“：”。二、第二种方法：切换至QQ输入法（其它中文汉字输入法的方法类似），右键点击输入法状态栏，菜单内点击“符号输入”，子菜单内点击“特殊符号”。三、打开符号输入器后，进入“标点符号”页，点击“：”即可输入。四、第三种方法：在Office下的软件内（Word、Excel、PPT等），点击“插入”。五、接着点击“符号”，下拉菜单内点击“更多”。六、进入“标点符号”页面，双击其中的三个“：”即可输入（三种帽号分别是英文帽号、中文半角帽号、中文全角帽号）。

Fifth, the age factor has resulted in with the second language custom since the 1970s, as representative"s overseas speech education expert and the scholar the influence which results to the second language custom has conducted the massive research take US language expert Krashen to the age, the findings was still different people have different views, different people have different views. At present tends the mutual recognition has the following several points: 11 study speed question. Because in intelligence aspect adults and so on growth level, aspect of knowledge, social experience and mother tongue ability occupies the big superiority, adult"s study speed, specially grammar study speed, greatly quickly in child. But accumulates gradually along with the language and gradually influences, the child will pursue finally on and surpasses the adult. The child will demonstrate in the natural language environment the big second language custom will result in the superiority, but in the regular foreign language classroom because of condition and so on linguistic environment, intelligence level of development limits, the study speed will compare the adult to be slow. 21 intonation questions. Under non-regular study condition, (also only then the child can achieve with speaks mother tongue"s person"s same intonation, the child generally before 6 years old has scholar to think before the puberty, before namely 12, 13 year old of ), if can receive the enough foreign language to gradually influence, has the possibility to achieve the pronunciation to be pure. The adult undergoes many year regular studies, most may speak the foreign language fluently, but only then few people can achieve with speak mother tongue"s person similar or the same intonation. 31 verbal skill and potential question. The child has obtains with speaks the mother tongue same verbal skill the potential. Grasps the speed with the pronunciation to compare, the child grasps to the foreign language syntax rules is relatively slow, can master the syntax rules well approximately about 15 years old. In oral and written language aspect, grown-up average per person may achieve speaks the mother tongue level, the precision which the grammar grasps may achieve or surpass speaks mother tongue"s person. Whether regardless to achieve finally speaks mother tongue"s verbal skill similarly, the child compares in the pronunciation and the grammar aspect and the adult has the possibility to achieve a higher level and the level. 41 to pronunciation and grammar influence question. The age factor does not have the substantive influence to the foreign language grammar learning process, but has the decisive influence to the pronunciation custom. Just like we study the elaboration in the preceding text, in the second language custom results in the process, in the individual difference factor"s disposition factor, the verbal skill tendency factor, the academic motivation factor, the cognition style factor and the age factor result in the influence to the learner second language"s custom to be big. But speaking of the present research results, we were still unable to explain that which individual difference the factor the success very important function which results to the second language custom. In addition, we should also realize that to besides the individual difference factor, the society, the foreign language custom results in the mechanism, the cultural context, the study atmosphere and the environment and so on results in the influence to the learner second language custom to be also big. We study the discussion the individual difference factor are merely affect the learner second language to practice one of numerous factors.

你设置了什么就包括什么啊？

factors which influence the development of economy

"not meaningful for factors对因素没有意义

首先，明确String与Factor的区别。String是字符串，可用于记录琐细信息（比如发现UFO者的口头描述内容）。Factor是因此，用于给一行记录做“分类标记”，比如人的性别factors可以设置为“男”、“女”，工作效率最高日期的factors可以是“Mon”、"Tue"，对于工作效率也可以有“high”、“low”等。对于Factor类型属性，R语言可以自动统计数据的factor水平（level），比如，男，有多少，Mon有多少等。stringsAsFactors = F意味着，“在读入数据时，遇到字符串之后，不将其转换为factors，仍然保留为字符串格式”。plus：在读入数据框之后，仍然有机会可以对数据框的列进行factors转换的操作。

In my opinion,there are some facters for the personal success. Wuxing,my good friend, was succeeded in learning Japanese.she has won many prizes up to now.However,her success doesn"t come by chance.she also had a loss,but she thought failure is not an ending.It was necessary for her to find out the cause of failure.She always worked hard with an iron-will.Finally, she got rid of a lot of trouble.As a matter of course, i shoud learn her spirit of persisting in overcoming difficulties to acquire her goal.

先按回车下面的shift再按键盘字母上第四 就有了 你看 ￥

仔细看看语法书 having been done 和 done 同时出现时 用 done ，havingbeendone 一般避免使用

这问题罗列就可以知道答案了，楼主的想法可能是把数字分解后用指数相加，72=3^2*2^3，但是这样做没什么依据，如果你有学排列组合的话就好办多了，72可以分解为2个3和3个2相乘，因数的个数就是3*4=12个，因为因数肯定可以分解为多少个3和多少个2,3的取法有3种，2的取法有4种，所以是12个

multiple factors 多对因子[例句]Multiple factors will amplify the effects of global warming on agriculture and forestry.多种因素将会增加大全球暖化对农业和林业的影响。

设方程x^4+1=0的根为a+bi,a,b∈R，则(a+bi)^4+1=0,所以(a^4-6a^2b^2+b^4+1)+(4a^3b-4ab^3)i=0,所以a^4-6a^2b^2+b^4+1=0（1）4a^3b-4ab^3=0（2）由(2)得，4ab(a+b)(a-b)=0,所以a=0或b=0或a=b或a=-b把a=0或b=0代入(1)得，方程无解。把a=b代入(1)得，a=b=√2/2或a=b=-√2/2把a=-b代入(1)得，a=√2/2，b=-√2/2或a=-√2/2，b=√2/2所以方程x^4+1=0的解为：x1=√2/2+√2/2ix2=-√2/2-√2/2ix3=√2/2-√2/2ix4=-√2/2+√2/2i

这个可以直接单独下载一个各种图标大全的软件才能打出来

激励因素Hygiene factors are the factors that seem to make individuals feel dissatisfied with their jobs.激励因素是使个人对工作感觉满意的因素。

一、动词＋介词agreewith同意beginwith以……开始comefrom来自arrivein／at到达feellike想要looklike看起来像playwith玩耍geton上车getoff下车falloff跌落getto到达fallbehind落后hearfrom收到……的来信hearof听说knockat敲（门）laughat嘲笑lookat看lookafter照看listento听lookfor寻找sendfor派人去叫thinkof想到thinkabout考虑waitfor等候shoutat对……大喊大叫payfor付款dowith处置；对付fillwith用……装满leavefor前往二、动词＋副词A?及物eatup吃光giveup放弃；停止lookup查寻pickup拾起；捡起putup建立；举起ringup打电话wakeup唤醒tieup捆绑起来dressup乔装打扮hurryup赶快sendup发射getin收获handin上交findout查出；查明sellout卖完workout解出；算出lookover检查thinkover考虑putdown放下takedown拿下；取下writedown写下；记下turndown调小；关低puton穿戴；上演tryon试穿turnon打开takeaway取走；拿走putaway放好sendaway撵走moveaway搬走takeoff脱掉turnoff关闭getback回来giveback归还B．不及物的comein进来comeon快；加油comeout出来；（花）开comealong走吧comeover过来；顺便来comeround（走）过来fallover（向前）摔倒getup起床goon继续growup成长；长大gohome回家hurryoff匆匆离开lookaround四处看看takeoff起飞lookout当心sitdown坐下holdon不挂断；等一等wakeup醒来三、动词＋副词＋介词catchupwith赶上goonwith继续dowellin在……方面做得好workhardat努力学习／工作getonwith与……相处pull．．．upfrom．．．把……从……拉出来四、动词＋名词＋介词takecareof照料；照顾makesureof弄确切haveadrinkof喝一点haveawordwith与……交谈havealookat看一看makefriendswith与……交朋友五、系动词＋形容词＋介词be（feel）afraidof害怕beangrywith生气bebusywith忙于……begoodat擅长befullof充满be（become）interestedin对……感兴趣belatefor迟到bestrictwithsb．对某人严格要求bestrictinsth．对某事严格要求bebad／goodfor对……有害／益beshortfor是……的简称bedifferentfrom与……不同bereadyfor为……做好准备beworriedabout对……担心becoveredwith被……覆盖befriendlyto对……友好

[00:01.12]Macy Gray - The Sellout[00:05.89][00:32.16]There I am and where I go, [00:34.26]what I do and who I know, [00:37.54]yeah, take a picture [00:39.36]"cause it"s always changing [00:41.85][00:42.40]But I wanna hold on to you [00:44.99]Yes, I wanna hold on to you [00:47.62]But you"re slippery like the gasoline [00:50.49]and you feel like fire [00:52.87]And I"m out on a limb [00:57.26]I"m giving in [00:59.91]I"m selling out to the pay, to the show [01:05.27]This is my gimmick and I wanna win it [01:10.71]I"m selling out [01:12.68]I won"t fight you no more [01:14.41][01:14.89]Honey babe and honey boo, [01:17.34]I always pictured you by my side forever [01:22.24]And I can"t believe that you"re gone now [01:25.40]"cause I got a love to give [01:27.61]Yes, I got a love to give [01:30.63]I got something you should see [01:33.15]Baby, just come back to me "cause I, [01:36.25][01:37.33]I"m out on a limb and I"m giving in [01:42.46]I"m selling out to the pay, to the show [01:47.89]This is my gimmick and I wanna win it [01:53.30]I"m selling out [01:55.32]I won"t fight you no more [01:57.61][01:58.40]Oh, don"t go away [02:00.89]I want you to stay [02:03.61]I"m-a sing you a song [02:05.52]Listen to my song and I hope that you like it [02:09.01]Oh, don"t go away [02:11.62]I want you to stay [02:14.27]I"m will sing you a song [02:15.82]Listen to my song and I hope that you like it [02:18.59][02:19.14]Hey, everybody gather "round for me [02:21.39]I know I ain"t the same as I used to be (Used to be) [02:23.99]But there are things that I really need (Really need) [02:26.71]There"s some people that I wanna meet [02:28.98]So, one (One), two (Two), [02:30.67]three, let"s go (Three, let"s go), [02:32.18]four (Four), five (Five), to the show [02:34.56]Nursery rhymes and lullabies gonna make you [02:39.17]dance but I cry "cause I, [02:40.22][02:41.13]I"m out on a limb and I"m giving in [02:46.56]I"m selling out to the pay, to the show [02:51.92]This is my gimmick and I wanna win it [02:57.39]I"m selling out [02:59.17]I won"t fight you no more [03:02.68]I"m out on a limb and I"m giving in [03:08.11]I"m selling out for (To the) pay, [03:11.14]for (To the) show [03:13.23]This is my gimmick and I wanna win it [03:18.57]I"m selling out [03:19.75]I won"t fight you no more [03:23.21](Oh, don"t go away) [03:26.38]Won"t fight you no more [03:29.17](I"m-a sing you a song [03:30.75]Listen to my song and I hope that you like it) [03:31.83]Won"t fight you no more [03:34.48](Oh, don"t go away [03:37.00]I want you to stay) [03:37.66]I wanna win it [03:39.85](I"m-a sing you a song [03:41.12]Listen to my song and I hope that you like it)[03:45.81]

把问题说具体，大家才好回答，像你这样问的话就只能用锤子打了。