题干

如图,在平面直角坐标系中,抛物线y=ax2+bx+c(a≠0)的图象经过M(1,0)和N(3,0)两点,且与y轴交于D(0,3),直线l是抛物线的对称轴.

(1)求该抛物线的解析式.
(2)若过点A(﹣1,0)的直线AB与抛物线的对称轴和x轴围成的三角形面积为6,求此直线的解析式.
(3)点P在抛物线的对称轴上,⊙P与直线AB和x轴都相切,求点P的坐标.

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答案(点此获取答案解析)

解:(1)∵抛物线y=ax2+bx+c(a≠0)的图象经过M(1,0)和N(3,0)两点,且与y轴交于D(0,3),
∴假设二次函数解析式为:y=a(x-1)(x-3),
将D(0,3),代入y=a(x-1)(x-3),
得:3=3a,∴a=1,
∴抛物线的解析式为:y=a(x-1)(x-3)=x2-4x+3;
(2)∵过点A(-1,0)的直线AB与抛物线的对称轴和x轴围成的三角形面积为6,

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阅读理解

    The resignation(辞职)letter of Gu Shaoqiang, a teacher from Henan, “The world is so big; I want to see it.” is very popular in the Internet. Many people say that it spoke the minds of millions of people who feel they have been in a boring and normal life and want to do something different to change it. Whatever the teacher may be able to achieve with her life, it is meaningful for people to make their dream come true.

    So, what is your opinion? Should we praise(表扬)the teacher for resigning and following her dreams? 

    Yes---All of us have dreams that can't come true right now. 

    First, Too many people waste their lives by doing things they don't love simply because it is what people expect them to do. They are not happy and they also affect(影响) people around them. The earlier they can break free, the more meaning they can make out of their lives. 

    Second, It is a waste of people's talents and social resources(资源) if they don't get to do the things they are most talented at. Some people don't want to be white-collar workers all their lives. They should have the freedom to change their lives. 

    Third, As our country develops so fast, people have greater freedom to change their lives as long as they put in the time and effort. The teacher is a good example. 

    No---People can't change their lives overnight. 

    First, “Seeing the world” is not good enough an excuse to leave one's job and life. This kind of attitude could actually be a bad example for young people.

    Second, Everyone has a place in society and life. People may not have achieved their wildest or most ambitious dreams, but where they end up is the result of their and society's decisions. Unless they offer to make lots of efforts and sacrifices, people can't change their lives overnight. 

    Third, The reason why the teacher gave up her job is too unclear. It is too irresponsible.