11平行四边形的存在性问题解题策略[1].doc

04平行四边形的存在性问题解题策略12021陕西西安如图，在平面直角坐标系中，抛物线经过A1，0，B3，0，C0，1三点。 1求该抛物线的表达式； 2点Q在y轴上，点P在抛物线上，要使以点Q、P、A、B为顶点的四边形是平行四边形，求所有满足条件的点P的坐标。【答案】解：1设该抛物线的表达式为。根据题意，得、解之，得所求抛物线的表达式为 2当AB为边时，只要PQ/AB，且PQ=AB=4即可，又知点Q在y轴上，点P的横坐标为4或-4，这时，将合条件的点P有两个，分别记为P1，P2。而当x=4时，此时当AB为对角线时，只要线段PQ与线段AB互相平分即可，又知点Q在y轴上，且线段AB中点的横坐标为1，点P的横坐标为2，这时，符合条件的点P只有一个，记为P3，而当x=2时，y=-1，此时P32，-1综上，满足条件的点1. 2021山东威海，25，12分如图，抛物线交轴于点，点,交轴于点点C是点A关于点B的对称点，点F是线段BC的中点，直线过点F且与轴平行直线过点C，交轴于点D1求抛物线的函数表达式；2点K为线段AB上一动点，过点K作轴的垂线与直线CD交于点H，与抛物线交于点G,求线段HG长度的最大值；3在直线上取点M，在抛物线上取点N，使以点A，C，M，N为顶点的四边是平行四边形，求点N的坐标图 备用图【答案】 解：1设抛物线的函数表达式抛物线与轴交于点，将该点坐标代入上式，得所求函数表达式，即2点C是点A关于点B的对称点，点，点，点C的坐标是将点C的坐标是代入，得直线CD的函数表达式为设K点的坐标为，那么H点的坐标为，G点的坐标为点K为线段AB上一动点，当时，线段HG长度有最大值3点F是线段BC的中点，点，点 ，点F的坐标为直线过点F且与轴平行，直线的函数表达式为点M在直线上，点N在抛物线上 ，设点M的坐标为，点N的坐标为点，点 ，分情况讨论： 假设线段AC是以点A，C，M，N为顶点的四边是平行四边形的边，那么须MNAC，且MNAC8当点N在点M的左侧时，解得N点的坐标为当点N在点M的右侧时，解得N点的坐标为假设线段AC是以点A，C，M，N为顶点的平行四边形的对角线，由“点C与点A关于点B中心对称知：点M与点N关于点B中心对称取点F关于点B对称点P，那么点P的坐标为过点P作NP轴，交抛物线于点N将代入，得过点N，B作直线NB交直线于点M在BPN和BFM中，BPNBFMNBMB四边形点ANCM为平行四边形坐标为的点N符合条件当点N的坐标为，时，以点A，C，M，N为顶点的四边是平行四边形2、2021重庆綦江如图，抛物线经过点，抛物线的顶点为，过作射线过顶点平行于轴的直线交射线于点，在轴正半轴上，连结1求该抛物线的解析式；2假设动点从点出发，以每秒1个长度单位的速度沿射线运动，设点运动的时间为问当为何值时，四边形分别为平行四边形？直角梯形？等腰梯形？xyMCDPQOAB3假设，动点和动点分别从点和点同时出发，分别以每秒1个长度单位和2个长度单位的速度沿和运动，当其中一个点停止运动时另一个点也随之停止运动设它们的运动的时间为，连接，当为何值时，四边形的面积最小？并求出最小值及此时的长*26解：1抛物线经过点，1分二次函数的解析式为：3分2为抛物线的顶点过作于，那么，4分xyMCDPQOABNEH当时，四边形是平行四边形5分当时，四边形是直角梯形过作于，那么如果没求出可由求6分当时，四边形是等腰梯形综上所述：当、5、4时，对应四边形分别是平行四边形、直角梯形、等腰梯形7分3由2及，是等边三角形那么过作于，那么8分=9分当时，的面积最小值为10分此时11分3.2021年内蒙古包头二次函数的图象经过点，直线与轴交于点1求二次函数的解析式；2在直线上有一点点在第四象限，使得为顶点的三角形与以为顶点的三角形相似，求点坐标用含的代数式表示；3在2成立的条件下，抛物线上是否存在一点，使得四边形为平行四边形？假设存在，请求出的值及四边形的面积；假设不存在，请说明理由yxOBADC(x=m)(F2)F1E1 (E2)yxO2612分解：1根据题意，得解得2分2当时，得或，当时，得，点在第四象限，4分当时，得，点在第四象限，6分3假设抛物线上存在一点，使得四边形为平行四边形，那么，点的横坐标为，当点的坐标为时，点的坐标为，点在抛物线的图象上，舍去，9分当点的坐标为时，点的坐标为，点在抛物线的图象上，舍去，12分注：各题的其它解法或证法可参照该评分标准给分4、2021柳州OxyABCD图11如图11，抛物线与轴的一个交点为，与y轴的负半轴交于点C，顶点为D1直接写出抛物线的对称轴，及抛物线与轴的另一个交点A的坐标；2以AD为直径的圆经过点C求抛物线的解析式；点在抛物线的对称轴上，点在抛物线上，且以四点为顶点的四边形为平行四边形，求点的坐标 解：1对称轴是直线：，点A的坐标是3，02分说明：每写对1个给1分，“直线两字没写不扣分2如图11，连接AC、AD，过D作于点M，解法一：利用点A、D、C的坐标分别是A 3，0，D1，、C0，AO3，MD=1由得 3分又4分由 得 5分函数解析式为： 6分 解法二：利用以AD为直径的圆经过点C点A、D的坐标分别是A 3，0 、D1，、C0， 3分又 4分由、得 5分函数解析式为： 6分3如下图，当BAFE为平行四边形时yxOABCD图11EF 那么，并且 =4，=4 由于对称为，点F的横坐标为57分将代入得，F5，12 8分根据抛物线的对称性可知，在对称轴的左侧抛物线上也存在点F，使得四边形BAEF是平行四边形，此时点F坐标为，12 9分当四边形BEAF是平行四边形时，点F即为点D，此时点F的坐标为1， 10分综上所述，点F的坐标为5，12， ，12或1，其它解法参照给分5、(2021烟台市) 如图，抛物线与轴交于两点，与轴交于C点，且经过点，对称轴是直线，顶点是（1） 求抛物线对应的函数表达式；（2） 经过两点作直线与轴交于点，在抛物线上是否存在这样的点，使以点为顶点的四边形为平行四边形？假设存在，请求出点的坐标；假设不存在，请说明理由；（3） 设直线与y轴的交点是，在线段上任取一点不与重合，经过三点的圆交直线于点，试判断的形状，并说明理由；（4） 当是直线上任意一点时，3中的结论是否成立？请直接写出结论OBxyAMC1英文版 easily blame, to prevent the broken window effect. Supervise the leading cadres to play an exemplary role, take the lead in the strict implementation of the < code > and < rule >, lead to safeguard the solemnity and authority of the party discipline, ensure that the party discipline and the laws and regulations for implementation in place. Throughout the discipline in the daily supervision and management, strengthen supervision and inspection, from the thorough investigation of violations of discipline behavior. Strengthen to key areas, key departments and key projects as well as the masses reflect the concentration of the units and departments for supervision. - strengthening supervision, discipline inspection and supervision of cadres to set an example for compliance with the < code > and < rule > is a man must be hexyl, blacksmith needs its own hardware. Discipline inspection organs as the executor of the party discipline, and supervisor of the defenders, for its supervision must be more strictly, discipline inspection and supervision of cadres to firmly establish the awareness of Party Constitution, sense of discipline and rules consciousness, politics loyalty, sense obey. Action speak Ji Ordinance to set an example of the regulations of the rule of law, strengthen supervision and accept the supervision of the firmness and consciousness, do comply with < > and < >. To firmly establish the discipline must first be disciplined, the supervisor will be subject to the supervision of "concept, and consciously safeguard and implement party compasses party, take the lead in practicing" three strict real strict, so loyal, clean, play. To be good at learning, the Constitution and the < code > as morality, politics and brought to fruition; to implement < >, do not want to, dare not, not with disciplinary ruler to supervision; to discipline a ruler, often the control inspection, and consciously in the ideological red line to draw the row Ming Good accumulation is indeed the bottom line, so that the heart has fear, said to have quit, the line has ended. Attached: indifferent to heart, calmly to the table in our life, there are many unpredictable things will happen, some good, some bad things, we cannot control is powerless to stop, but with time, you will find in life sometimes turns out to be not good, some bad things finally turned out to be a good thing, but then we muddy however did not know, this is the life teach us things. 1, life can be complex, can also be simple. Want simple life of precipitation, to have enough time to reflect, to make Become more perfect. Life is the most important thing is not to win, but the struggle; not to have conquered, but to have fought well. 2, the plain is the background of life. Live a plain life, give up on themselves is not a coward, but the wise answers; not disillusioned after the heart, such as ashes, but experience the storm after the enlightenment; not unrewarding perfunctorily, but calm attitude of life of unrestrained self-confidence. Plain living, there is no noise noisy, no earthly troubles, more did not fill in the discontent of desire, some just a calm, a calm. 3, memory of heart will not good things to erase the, life is a When no movie, pain is a beginning, the struggle is a kind of process, death is a kind of ending. Give up this giving up is the helpless, do not give up the abandoned, do not give up this giving up is ignorance, do not give up should not give up is persistent. 4, a thing figured is heaven, think impassability is hell. Since the living, to live better. Sometimes we because of too narrow-minded, too care around the chores and penny wise and pound foolish, not worth the candle. Some things to attract trouble and worry, completely depends on how we look at and deal with it. Don't always take everything back to things, and don't get into a blind alley, don't want to face, don't be narrow-minded. Poke to care, is a kind of open-minded, a free and easy. 5, I am not afraid of others behind me a knife, I afraid to look back and see stab me, is my intention to treat people; I am not afraid of the truth to tell the best friend, I'm afraid he turned to it as a joke to tell don't 6, when we are in a positive frame of mind, you will find many good things; and when we are in a negative state of mind, you will find many depressed things; life happy and worry, all is you of life attitude, optimistic, good luck; loss of sink, Eritrea company. When you are in adversity, may wish to change a point of view to think everything over to the good Think, because good mentality decided the fate of the! 7, people are tired, rest; heart tired, calm. Grow up, mature, this society read. Tired and sad, squat down, to their a hug. Because the world no one can sympathize with you, have mercy on you. You cry, tears is your own; you pain, no one can understand. Then you only tears to smile. 8, each people have youth,Each youth are a story, the life of the world never gets easier, I want what, wish the world all know, as has been the same; now want anything, for fear that others know, or like to lose the same. 9, the heart move, everything in the world is followed by birth, Rangrang, important thing is often the most difficult to open one's mouth, because words will reduce its importance; to let strangers people care about your life in the good things, the original is not easy 10, do not blame, do not laugh at who, also don't envy who. Like a person is a kind of feeling, not like a person is true. The truth is easy to explain, I feel Is unspeakable. The best travel life is that you in a strange place found a long lost touched. 11, happy life not in the bustling in, and in the peace of mind; no matter how many grievances, how uncomfortable, and ultimately to heal themselves or their own, others may got you to comfort, but never know your heart is how wanjianchuanxin. 12, ma'am, like a movie, learn to appreciate, learn to be grateful, learn tolerance, and goodness, helping others. Instead of accusing the society, as into one; and an exception is better to give than to what 13, don't envy him A sum of, don't lose your life and the life, respectively is: the former is a we experienced cannot escape in a day finally will last minute, while the latter is our persistent, we want to cherish the memory of those people and things. 14, learn to smile, learn to strong, the world you know so many people, so many people and you are, you cannot change also can't let everyone like you, so also do not want to do. Life is too short to go crazy to love to go to waste, to chase the dream to regret. 15, when temper, a blessing to go. A wounding elegant people, the key is to control their own emotions. With the mouth is the most stupid behavior. A control negative emotions than a can take a city more powerful water flow slow, language is expensive. People spent two years of time to learn to speak, but to spend a few years time to shut up. That is a kind of ability, that is a kind of wisdom. 16, life is not perfect, sometimes, growth is not a cry, not an eyeful of tears, there is no trace of emotion, there is no gleam of hope, no desire, no action, no static, there is only one kind of downward sinking feeling, sink A murky? 6? 7? 6? 7 sink? 6? 7? 6? 7 toward the bottom of the sink. 17, in some way, do not go, you will not know the other side scenery is beautiful. To you is not good, you do not mind too much, no one has an obligation to you; you learn knowledge, is you have weapons, you can start from scratch, but not unarmed; how do you treat people, does not represent how others treat you, if cannot see through this point, only inviting worry. 18, time is like a sponge in the water, as long as you are willing to squeeze, the total water is still there. Every life, after the ups and downs The best test of live, to life, survival and continuation, do not stop the struggle in the joys and sorrows of life on the road, so that different soul to bear life beat, acceptance of suffering. 19, indifferent to heart, calmly in table, elegant and comfortable life, do not take what is so important. The pursuit will be disappointed; to be alive, you will have trouble. Life is the most afraid of what all want to care about, but also what all grasp is not firm, without scenery, separated populations, such as not to desire, all docked in the fate of the end. Why is too rigid, the natural, to go stay not to live, let go of obsession, revel is 20, if the fate of the broken Hopes of sailing, please don't despair, the coast is still, if the fate of the withered petals of the beautiful, please do not sink, the spring is still, life will always be endless trouble, please don't helpless, because they are still alive, is still a dream, the sun still, we still. Lost, keep memories; to get, must work to; but the most important is good to cherish their own. 21, life, select the complex, is to choose the pain; choose a simple, is choose to be happy. The complex world like aSignificance of pride. Hope is the ornate palace, outside people admiring the magnificent, living in the deep knowledge of living it to pay the price. Simple world as a simple log cabin outside ridiculed shabby, the heart is willing to go live to know the joy. Suffering and joy is their own choice. 22, learn how to use a single powerful heart, let the past be the past, let the future come. Life is really the end of the end of an eagle is flying wings, life is constantly pursuit. Don't miss to regret, don't wait for old just miss. Time to return, seize every moment, again painstakingly again tired also Those struggling to fly. 23, life could not Yimapingchuan, even flat pavement, inevitably there will be a few pieces of roadblocks. Some of the rocks around the past, while others have to move it out. Just move others put the stone is very easy, because the stone from the appearance we can discern; difficult to myself to move away the heart of stone head. Leave time to spend with her, often reflect my heart, so as to remove your heart of stone. 24, everything does not have to be demanding, come to, everything does not have to care about, over the past; failing to do not frown, laugh it laugh. Results Don't demand, do to; life is a simple, calm and peaceful. Always not to choose their own path and regret, life is like a train, the scenery and then the United States will retreat, the passage of time and encounter will eventually drifting further and further away, before is always himself. 25, everyone has a weakness, weakness is true humanity. That has no weakness, a shallow person. That people think there is no weakness, mostly false. Life has shortcomings, there are shortcomings is the real life. That no one regret, or childish or numbness or Self deception. It is in tolerance of weakness and so on to accept, people live happily.Hello, everyone! I am a party member. The title of my speech is: < study and implement the party's two laws, doing practical play highway. 2021 October 18, the Central Committee of the Communist Party of China promulgated the implementation of the < the probity of the Communist Party of China self-discipline criterion > and < Chinese Communist Party discipline and punishment regulations. We Heyuan male passers-by to respond positively to the call of the Central Committee of the party, earnestly organize the study "party two regulations", truly gra