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如图,在平面直角坐标系xOy中,Rt△AOB的直角边OA在x轴正半轴上,OB在y轴负半轴上,且OA=3,OB=1,以点B为顶点的抛物线经过点A.
(1)求出该抛物线的解析式.
(2)第二象限内的点M,是经过原点且平分Rt△AOB面积的直线上一点.若OM=2,请判断点M是否在(1)中的抛物线上?并说明理由.
(3)点P是经过点B且与坐标轴不平行的直线l上一点.请你探究:当直线l绕点B任意旋转(不与坐标轴平行或重合)时,是否存在这样的直线l,在直线l上能找到点P,使△PAB与Rt△AOB相似(相似比不为1)?若存在,求出直线l的解析式;若不存在,说明理由.
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答案(点此获取答案解析)

解:(1)依题意得:A(3,0),B(0,﹣1),
∵B为抛物线的顶点,
∴设抛物线解析式为y=ax2﹣1,
将A坐标代入得:3a﹣1=0,即a=1

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        The stories we share with one another are important. They show wisdom and provide inspiration. They are important to our development. But sometimes people choose not to tell.

        Consider the negative effects of not sharing a story in the news: People are wondering if public health officials are holding back too much information about the recent outbreak of Ebola.

        There is a danger in holding back stories that ought to be told. Bobette Buster said it like this, “The fact is, history has shown us that stories not told can become like a dangerous genie (妖怪) left in a bottle. When they are finally uncorked,_their power to destroy is set free.”

        There are a number of reasons why we hide parts of our story: they often show our weaknesses or expose our disadvantages;they require courage and strength to share; and of course, there are some stories that should be kept secret—especially those that embarrass someone else.

        Most of us have two selves: the one we display on the outside and the one we actually are on the inside. And the better we get at hiding the stories that show our true selves, the more damage we may be causing to ourselves and to others.

       Honesty and openness is important:It proves we are trustworthy. It displays we are human. We are not perfect or better. It highlights the importance of hard work and personal development. Hard work may not allow us to overcome our disadvantages completely. But with hard work, we do not have to be restricted to our mistakes.

        Does this mean we admit every weakness, every disadvant­age and every secret regret to everybody we meet? No, of course not. There is a time and a place and a certain level of relationship necessary for some stories to be told in an appropriate manner.