问题 解答题

一开口向上的抛物线与x轴交于A,B两点,C(m,-2)为抛物线顶点,且AC⊥BC。

(1)若m是常数,求抛物线的解析式;

(2)设抛物线交y轴正半轴于D点,抛物线的对称轴交x轴于E点。问是否存在实数m,使得△EOD为等腰三角形?若存在,求出m的值;若不存在,请说明理由。

答案

24、解:(1)设抛物线的解析式为:

 

∵AC⊥BC,

由抛物线的对称性可知:△ACB为等腰直角三角形,又AB=4,

∴B(m+2,0)

代入,得a=

∴解析式为:

(2)由(1)得

设存在实数m,使得△EOD为等腰三角形。

∵△EOD为直角三角形,∴只能OD=OE。

∴当点E在x轴正半轴,即m>0时,

解得m=或m=(舍)。

当点E在x轴负半轴,即m<0时,

解得m=或m=(舍);

当点E在原点,即m=0时, B、O、D三点共线(不合题意,舍)

综上所述:存在实数m=或m=,使得△EOD为等腰三角形。

填空题

Old people are always saying that the young are not what they were. The same comment is made from generation to generation and it is always true. It has never been truer than it is today. The young are better (1)edu . They have a lot more money to spend and enjoy more freedom. They grow up more quickly and are not so (2)de on their parents. They think more for themselves and do not blindly (3)a the ideas of their (4)e . Events which the older generation remembers clearly are nothing (5)m than past history. This is as it should be. Every new generation is different from the one that preceded it. Today the difference is very marked indeed.
The old always assume that they know best for the simple reason (6)t they have been around a bit longer. They don’t like to feel that their values are being (7)qu or threatened. And this is precisely what the young are doing. They are questioning the assumptions of their elders and (8)dis their self-satisfaction. They take leave to doubt the older generation has created the best of all possible worlds. What they reject more than anything is conformity.
Who said that human differences can best be solved through conventional politics or by violent means Why have the older generation so often used (9)vi to their problems Why are they so unhappy and so troubled by a sense of guilt in their personal lives, so (10)oc with mean ambitions and the desire to accumulate more and (11)m material possessions Haven’t the old lost touch with all that is important in life
These are not questions the older generation can shrug off lightly. Their record over the past forty years or so hasn’t been exactly spotless. Traditionally, the young have (12)tu to their elders for guidance. Today, the situation might be (13)rev . The old—if they are prepared to admit it—could learn a thing or two from their children. One of the biggest lessons they could learn is that enjoyment is not "sinful". (14)En is a principle one could apply to all (15)as of life. It is surely not wrong to enjoy your work and enjoy your leisure. It is surely not wrong to live in the present rather than in the past or future.

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