promotion of employment, form a reasonable and orderly pattern of income distribution, build a more fair and sustainable social security systems, medical and health system reform. The plenary, innovation of social governance, must focus on the maintenance of fundamental interests of the overwhelming majority of the people, maximize factors, enhance social development, improving social governance, the interests of national security, ensure that the people live and work, social stability and order. To improve social governance, stimulating social organization, innovative and effective system of preventing and resolving social conflicts, improving the public security system, set up the National Security Council, national security systems and national security strategy to ensure national security. Plenary session, the construction of ecological civilization, you must establish systems of ecological system, using the system to protect the ecological environment. To improve natural resources asset property right system and use control, red line of delimitation of ecological protection, resources paid use system and ecological compensation system in ecological environment protection management system reform. Plenary session, centering on building a listening party command, can win and having a fine style of the people's army, a strong army under the new situation of the party Goals, restricting the development of national defense and army building is solved outstanding contradictions and problems, innovation and development of military theory, enhance military strategic guidance, improve the military strategy in the new period, building a modern military force system with Chinese characteristics. To deepen the adjustment of personnel system reform in the army, military policy and system reform, promote the development of military and civilian integration depth. Plenary session stressed that comprehensive reform must be to strengthen and improve the party's leadership, give full play to the core role of the party commands the overall situation and coordinating all parties, improving the party's leading water ... Margin. Challenged the leadership of the Communist Party of China, Marxism-Leninism and Mao Zedong thought by Deng Xiao-ping's flag, replaced by three representatives and the harmonic society. The former Communist Party spirit and social cohesion point of almost all political makeover. Characteristics of socialism public ownership is shifting to private ownership, planned regulation and market regulation, the proletarian regime controlled by the elite. Of universal equality, fairness and basic principles of distribution system is socialist society, however after economic monopolized by powerful, vested interests grow, employers do not have the same status, hardly seems fair social distribution. State key protection of capital interests rather than the interests of citizens, had been hits the bottom of the proletariat 2014年北京市各城区中考二模数学——代数综合题23题汇总
1、（2014年门头沟二模）23. 已知二次函数y??x2?2x?3图象的对称轴为直线． （1）请求出该函数图像的对称轴； y（2）在坐标系内作出该函数的图像；
（3）有一条直线过点p(1,5)，若该直线与二次函数 5y??x2?2x?3只有一个交点，
4请求出所有满足条件的直线的关系式.
3 2 1 -2-1O1234x -1
-22、（2014年丰台二模）23.如图,二次函数
y?x2?bx?cy经过点（-1,0）和点（0，-3）. 4（1）求二次函数的表达式；
3（2）如果一次函数y?4x?m的图象与二次函数的图21象有且只有一个公共点，求m的值和该公共点的坐标； （3）将二次函数图象y轴左侧部分沿y轴翻折，翻折后4321O1234x得到的图象与原图象剩余部分组成一个新的图象，该图12象记为G，如果直线y?4x?n与图象G有3个公共点，3求n的值. 4
3、（2014年平谷二模）23．已知关于x的一元二次方程x2?mx?m?1?0． （1）求证：无论m取任何实数时，方程总有实数根； （2）关于x的二次函数y1?x2?mx?m?1的图象C1经过
(k?1，k2?6k?8)和(?k?5，k2?6k?8)两点．
y①求这个二次函数的解析式；
②把①中的抛物线C1沿x轴翻折后，再向左平移2个
bviously, face China's Socialist system, the Communist Party is not the party. In that case, political chaos has been very tight. Is remodeling or reconstruction, is a correction or a stove. Whether to turn right or left, is back to the source or put forward new political ideas. This is to determine the road problems in China, is also the key out of the deep water of the reform of the economic system. After 18, the new Central collective leadership attaches great importance to political orientation. First, the \es\point, starting from the Central Government's self-restraint, which preaches and pro-image, brought fresh feeling to the community. Secondly, before reform and opening up and reform and opening two periods after non-negative, untying the tangle of the society a long time on this issue. Third, a new generation of party leaders on various occasions to Mao Ze-Dong and Mao Ze-Dong's thought of evaluation has room for manoeuvre, through to the ruling ideology of Mao Zedong thought, is the call of the soul to the Socialist Revolution and construction. Empty talks jeopardize national intereNew leaders both stressed the need to implement the Constitution, stressed the need to turn off the power in a cage. Also stresses that Mao Zedong thought cannot be lost, 30 years after the reform and opening up 30 years ago can not deny each other. Both advocate democracy and release \ven does not speak of\cal constraints. Neither deny the history of the CPC Central Committee on several issues ...Comrades: today brings together members, mainly in order to provide a platform to Exchange and learn from each other in order to facilitate our work. Just now, we focus on taxation, planning and stability, safety, project construction, typical topics such as private facts presentation and interaction, and towns currently exist in the in-depth analysis of the problems to be solved, to explore new methods to solve the problem. It can be said that summing up the achievement, no grandstanding; analysisOx备用图单位，向上平移8个单位得到抛物线C2．设抛物线C2交x轴于M、N两点（点M在点
N的左侧），点P(a，b)为抛物线C2在x轴上方部分图象上的一个动点.当∠MPN≤45°
时，直接写出a的取值范围．
4、(2014年顺义二模) 23．已知关于x的一元二次方程mx2?4x?4?m?0． （1）求证：方程总有两个实数根；
（2）若m为整数，当此方程有两个互不相等的负整数根时，求m的值；
（3）在（2）的条件下，设抛物线y?mx2?4x?4?m与x轴交点为A、B（点B在点A的
右侧），与y轴交于点C．点O为坐标原点，点P在直线BC上，且OP=
12BC，求点P的坐标．
5、（2014年石景山二模）23. 关于x的一元二次方程x2?3(m?1)x?3m?2?0． （1）求证：无论m为何值时，方程总有一个根大于0；
（2）若函数y?x2?3(m?1)x?3m?2与x轴有且只有一个交点，求m的值； （3）在（2）的条件下，将函数y?x2?3(m?1)x?3m?2的图象沿直线x?2翻折，得
到新的函数图象G．在x，y轴上分别有点P(t，0)，Q(0，2t)，其中t?0，当线
段PQ与函数图象G只有一个公共点时，求t的值．
解：
6、（2014年海淀二模）23．已知关于x的方程：
yx2?(m?1)x?m?05①和x2?(9?m)x?2(m?1)?3②，其
43中m?0.
21（1）求证：方程①总有两个不相等的实数根；
-5-4-3-2-1O12345（2）设二次函数y21x1?x?(m?1)x?m的图象与x轴交于
--2A、B两点（点A在点B的左侧），将A、B两点-3-4按照相同的方式平移后，点A落在点A'(1,3)处，点B-5落在点B'处，若点B'的横坐标恰好是方程②的一个
根，求m的值；
（3）设二次函数y22?x?(9?m)x?2(m?1)，在（2）的条件下， 函数y1，y2的图象
位于直线x?3左侧的部分与直线y?kx（k?0）交于两点，当向上平移直线y?kx时，交点位置随之变化，若交点间的距离始终不变，则k的值是________________.
s an affirmation of Deng Xiao-ping's reform ideas. These strong political signal showing a new generation of political leaders is still keeping to the Socialist road. Four is revisiting the \o Ze-Dong's historical cycle of\ofile anti-corruption and the importance of the Constitution, reorganization is bad style of officialdom, was to civilize people obey the law, while improving the color change of the regime of vigilance. Five is to reform into deeper waters and stressed that top-level design, this is a review on the reform and opening up in the past, is also looking for a way out. Six foreign and Russia closer, the flexible attitude on the issue of the Korean peninsula, Sino-Japanese fishing hardline China on the island out of the \ent\ow profile shadow began to gradually plan development. Signs show that the new leadership began to make a left turn in politics. However, as of right now, not only ideological confusion in the community, the new leadership's thinking is messy. sts and try again, ipromotion of employment, form a reasonable and orderly pattern of income distribution, build a more fair and sustainable social security systems, medical and health system reform. The plenary, innovation of social governance, must focus on the maintenance of fundamental interests of the overwhelming majority of the people, maximize factors, enhance social development, improving social governance, the interests of national security, ensure that the people live and work, social stability and order. To improve social governance, stimulating social organization, innovative and effective system of preventing and resolving social conflicts, improving the public security system, set up the National Security Council, national security systems and national security strategy to ensure national security. Plenary session, the construction of ecological civilization, you must establish systems of ecological system, using the system to protect the ecological environment. To improve natural resources asset property right system and use control, red line of delimitation of ecological protection, resources paid use system and ecological compensation system in ecological environment protection management system reform. Plenary session, centering on building a listening party command, can win and having a fine style of the people's army, a strong army under the new situation of the party Goals, restricting the development of national defense and army building is solved outstanding contradictions and problems, innovation and development of military theory, enhance military strategic guidance, improve the military strategy in the new period, building a modern military force system with Chinese characteristics. To deepen the adjustment of personnel system reform in the army, military policy and system reform, promote the development of military and civilian integration depth. Plenary session stressed that comprehensive reform must be to strengthen and improve the party's leadership, give full play to the core role of the party commands the overall situation and coordinating all parties, improving the party's leading water ... Margin. Challenged the leadership of the Communist Party of China, Marxism-Leninism and Mao Zedong thought by Deng Xiao-ping's flag, replaced by three representatives and the harmonic society. The former Communist Party spirit and social cohesion point of almost all political makeover. Characteristics of socialism public ownership is shifting to private ownership, planned regulation and market regulation, the proletarian regime controlled by the elite. Of universal equality, fairness and basic principles of distribution system is socialist society, however after economic monopolized by powerful, vested interests grow, employers do not have the same status, hardly seems fair social distribution. State key protection of capital interests rather than the interests of citizens, had been hits the bottom of the proletariat
7、（2014年西城二模）23．经过点（1，1）的直线l：y?kx?2 (k?0)与反比例函数
Gm1:y1?x (m?0)的图象交于点A(?1,a)，B（b，-1），与y轴交于点D． （1）求直线l对应的函数表达式及反比例函数G1的表达式；
（2）反比例函数Gt2::y2?x (t?0)，
①若点E在第一象限内，且在反比例函数G2的图象上，若EA=EB，且△AEB的面积为8，求点E的坐标及t值；
②反比例函数G2的图象与直线l有两个公共点M，N（点M在点N的左侧），若DM?DN?32，直接写出t的取值范围．
8、（2014年通州二模）无
9、（2014年东城二模）23．已知：关于x的一元二次方程
mx2?(m?3)x-3?0．
（1）求证：无论m取何值，此方程总有两个实数根； （2）设抛物线y?mx2?(m?3)x-3，证明：此函数图像一
定过x轴，y轴上的两个定点（设x轴上的定点为点A，
y轴上的定点为点C）；
（3）设此函数的图像与x轴的另一交点为B，当△ABC为锐角三角形时，求m的取值范围．
10、（2014年朝阳二模）23．在平面直角坐标系xOy中，
yN点P(m，0)为x轴正半轴上的一点，过点P做x轴的垂
线，分别交抛物线y=-x2+2x和y=-x2
+3x于点M，N．
MOPxbviously, face China's Socialist system, the Communist Party is not the party. In that case, political chaos has been very tight. Is remodeling or reconstruction, is a correction or a stove. Whether to turn right or left, is back to the source or put forward new political ideas. This is to determine the road problems in China, is also the key out of the deep water of the reform of the economic system. After 18, the new Central collective leadership attaches great importance to political orientation. First, the \es\point, starting from the Central Government's self-restraint, which preaches and pro-image, brought fresh feeling to the community. Secondly, before reform and opening up and reform and opening two periods after non-negative, untying the tangle of the society a long time on this issue. Third, a new generation of party leaders on various occasions to Mao Ze-Dong and Mao Ze-Dong's thought of evaluation has room for manoeuvre, through to the ruling ideology of Mao Zedong thought, is the call of the soul to the Socialist Revolution and construction. Empty talks jeopardize national intereNew leaders both stressed the need to implement the Constitution, stressed the need to turn off the power in a cage. Also stresses that Mao Zedong thought cannot be lost, 30 years after the reform and opening up 30 years ago can not deny each other. Both advocate democracy and release \ven does not speak of\cal constraints. Neither deny the history of the CPC Central Committee on several issues ...Comrades: today brings together members, mainly in order to provide a platform to Exchange and learn from each other in order to facilitate our work. Just now, we focus on taxation, planning and stability, safety, project construction, typical topics such as private facts presentation and interaction, and towns currently exist in the in-depth analysis of the problems to be solved, to explore new methods to solve the problem. It can be said that summing up the achievement, no grandstanding; analysis（1）当m?12时， MNPM?_____； （2）如果点P不在这两条抛物线中的任何一条上．当四条
线段OP，PM，．PN，MN中恰好有三条线段相等时， 求m的值．
11、（2014年密云二模）23. 已知P（﹣3，m）和Q（1，m）是抛物线y=2x2
+bx+1上的两点．
（1）求b的值;
（2）判断关于x的一元二次方程2x2
+bx+1=0是否有实数根，若有，求出它的实数根；若没有，请说明理由;
（3）将抛物线y=2x2
+bx+1的图象向上平移k（k是正整数）个单位，使平移后的图象与x轴无交点，求k的最小值．
12、（2014年延庆二模）
13、(2014年房山二模) 23. 已知关于x的一元二次方程x2?3x?k?1?0有实数根，k为正整数.
（1）求k的值；
（2）当此方程有两个不为0的整数根时，将关于x的二次函数y?x2?3x?k?1的图象向下平移2个单位，求平移后的函数图象的解析式；
（3）在（2）的条件下，将平移后的二次函数
图象位于y轴左侧的部分沿x轴翻折，图象的其余部分保持不变，得到一个新的图象G．当直线y?5x?b与图象G有3个公共点时，请
s an affirmation of Deng Xiao-ping's reform ideas. These strong political signal showing a new generation of political leaders is still keeping to the Socialist road. Four is revisiting the \o Ze-Dong's historical cycle of\ofile anti-corruption and the importance of the Constitution, reorganization is bad style of officialdom, was to civilize people obey the law, while improving the color change of the regime of vigilance. Five is to reform into deeper waters and stressed that top-level design, this is a review on the reform and opening up in the past, is also looking for a way out. Six foreign and Russia closer, the flexible attitude on the issue of the Korean peninsula, Sino-Japanese fishing hardline China on the island out of the \ent\ow profile shadow began to gradually plan development. Signs show that the new leadership began to make a left turn in politics. However, as of right now, not only ideological confusion in the community, the new leadership's thinking is messy. sts and try again, ipromotion of employment, form a reasonable and orderly pattern of income distribution, build a more fair and sustainable social security systems, medical and health system reform. The plenary, innovation of social governance, must focus on the maintenance of fundamental interests of the overwhelming majority of the people, maximize factors, enhance social development, improving social governance, the interests of national security, ensure that the people live and work, social stability and order. To improve social governance, stimulating social organization, innovative and effective system of preventing and resolving social conflicts, improving the public security system, set up the National Security Council, national security systems and national security strategy to ensure national security. Plenary session, the construction of ecological civilization, you must establish systems of ecological system, using the system to protect the ecological environment. To improve natural resources asset property right system and use control, red line of delimitation of ecological protection, resources paid use system and ecological compensation system in ecological environment protection management system reform. Plenary session, centering on building a listening party command, can win and having a fine style of the people's army, a strong army under the new situation of the party Goals, restricting the development of national defense and army building is solved outstanding contradictions and problems, innovation and development of military theory, enhance military strategic guidance, improve the military strategy in the new period, building a modern military force system with Chinese characteristics. To deepen the adjustment of personnel system reform in the army, military policy and system reform, promote the development of military and civilian integration depth. Plenary session stressed that comprehensive reform must be to strengthen and improve the party's leadership, give full play to the core role of the party commands the overall situation and coordinating all parties, improving the party's leading water ... Margin. Challenged the leadership of the Communist Party of China, Marxism-Leninism and Mao Zedong thought by Deng Xiao-ping's flag, replaced by three representatives and the harmonic society. The former Communist Party spirit and social cohesion point of almost all political makeover. Characteristics of socialism public ownership is shifting to private ownership, planned regulation and market regulation, the proletarian regime controlled by the elite. Of universal equality, fairness and basic principles of distribution system is socialist society, however after economic monopolized by powerful, vested interests grow, employers do not have the same status, hardly seems fair social distribution. State key protection of capital interests rather than the interests of citizens, had been hits the bottom of the proletariat 你直接写出b的取值范围.
14、（2014年昌平二模）23．已知抛物线y?ax2?(3a?1)x?2(a?1)(a?0).
（1）求证：无论a为任何非零实数，该抛物线与x轴都有交点；
17、（2014年燕山二模）23. 已知关于x的一元二次方程
x2?2(k?1)x?k2?2k?3?0有两个不相等的实数
根．
（1）求k的取值范围；
（2）当k取最小的整数时，求抛物线 y?x2?2(k?1)x?k2?2k?3的
（2）若抛物线y?ax2?(3a?1)x?2(a?1)与x轴交于A(m,0)、 B（n,0）两点，m、n、
a均为整数，一次函数y=kx+b(k≠0)的图象经过点P(n－l，n＋l）、Q(0,a），求一次函数
的表达式.
15、（2014年怀柔二模）23．如图，抛物线y=
与x轴交于A、B两点（点
A在点B的左侧），与y轴交于点C． （1）求点A、B的坐标；
（2）设D为y轴上的一点，当△ACD的面积等于△ACB的面积时，求D点的坐标； （3）已知：直线y=?k4x?k(k>0)交x轴于点E，M为直线上的动点，当以A、B、M为顶点所作的直角三角形有且只有四个时，求k的取值范围．
y C AOBx
16、（2014年大兴二模）23．已知：关于x的一元二次方程(k2?1)x2?(3k?1)x?2?0. （1）当方程有两个相等的实数根时，求k的值；
（2）若k是整数，且关于x的一元二次方程(k2?1)x2?(3k?1)x?2?0有两个不相等的整
数根时，把抛物线y?(k2?1)x2?(3k?1)x?2向右平移12个单位长度，求平移后抛物线的顶点坐标．
bviously, face China's Socialist system, the Communist Party is not the party. In that case, political chaos has been very tight. Is remodeling or reconstruction, is a correction or a stove. Whether to turn right or left, is back to the source or put forward new political ideas. This is to determine the road problems in China, is also the key out of the deep water of the reform of the economic system. After 18, the new Central collective leadership attaches great importance to political orientation. First, the \es\point, starting from the Central Government's self-restraint, which preaches and pro-image, brought fresh feeling to the community. Secondly, before reform and opening up and reform and opening two periods after non-negative, untying the tangle of the society a long time on this issue. Third, a new generation of party leaders on various occasions to Mao Ze-Dong and Mao Ze-Dong's thought of evaluation has room for manoeuvre, through to the ruling ideology of Mao Zedong thought, is the call of the soul to the Socialist Revolution and construction. Empty talks jeopardize national interests and try again, is an affirmation of Deng Xiao-ping's reform iNew leaders both stressed the need to implement the Constitution, stressed the need to turn off the power in a cage. Also stresses that Mao Zedong thought cannot be lost, 30 years after the reform and opening up 30 years ago can not deny each other. Both advocate democracy and release \ven does not speak of\Comrades: today brings together members, mainly in order to provide a platform to Exchange and learn from each other in order to facilitate our work. Just now, we focus on taxation, planning and stability, safety, project construction, typical topics such as private facts presentation and interaction, and towns currently exist in the in-depth analysis of the problems to be solved, to explore new methods to solve the problem. It can be said that summing up the achievement, no grandstanding; analysis2014年北京市各城区中考二模数学——代数综合题23题汇总 共 3 页
顶点坐标以及它与x轴的交点坐标； 3）将(2)中求得的抛物线在x轴下方的 部分沿x轴翻折到x轴上方，图象的 其余部分不变，得到一个新图象． 请你画出这个新图象，并求出新图象
与直线y?x?m有三个时m的值．
political signal showing a new generation of political leaders is still keeping to the Socialist road. Four is revisiting the \o Ze-Dong's historical cycle of\ofile anti-corruption and the importance of the Constitution, reorganization is bad style of officialdom, was to civilize people obey the law, while improving the color change of the regime of vigilance. Five is to reform into deeper waters and stressed that top-level design, this is a review on the reform and opening up in the past, is also looking for a way out. Six foreign and Russia closer, the flexible attitude on the issue of the Koreaher deny the history of the CPC Central Committee on several issues ...
不
同nese fishing hardline China on the island out of the \ent\ow profile shadow began to gradually 公共点hat the new leadership began to make a left turn in politics. However, as of right now, not only ideological confusion in the community, the new leadership's thinking is messy. 第 3 页（
deas. These strong n peninsula, Sino-Japaplan development. Signs show tcal constraints. Neit