题干

如图,直线y=﹣x+3与x轴交于点C,与y轴交于点A,点B的坐标为(2,3)抛物线y=﹣x2+bx+c经过A、C两点.

(1)求抛物线的解析式,并验证点B是否在抛物线上;

(2)作BD⊥OC,垂足为D,连接AB,E为y轴左侧抛物线点,当△EAB与△EBD的面积相等时,求点E的坐标;

(3)点P在直线AC上,点Q在抛物线y=﹣x2+bx+c上,是否存在P、Q,使以A、B、P、Q为顶点的四边形为平行四边形?若存在,直接写出点P的坐标;若不存在,请说明理由.

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答案(点此获取答案解析)

解:(1)在y=﹣x+3中,

令x=0,得y=3;令y=0,得x=3,

∴A(0,3),C(3,0).

∵抛物线y=﹣x2+bx+c经过A、C两点,

c=3

同类题2

阅读下面短文,掌握其大意,然后从41-60各题所给的四个选项(A、B、C、D)中,选出最佳选项。

    Mrs. Jones was over eighty, but she still drove her old car like a woman half her age. She loved driving very fast, and was proud of the fact 1 she had never, in her thirty-five years of driving, been punished 2 a driving offence (犯规,犯法).

    Then one day she nearly3 her record. A police car 4 her, and the policemen in it saw her5 a red light without stopping. Of course, she was stopped. It seemed 6 that she would be punished.

    7 Mrs. Jones came up to the judge, he looked at her seriously and said that she was  8 old to drive a car, and that the 9 why she had not stopped at the red 10was most probably that her eyes had become weak 11 old age, so that she had simply not seen it.

    When the judge had finished what he was 12, Mrs. Jones opened the big handbag she was 13 and took out her sewing. Without saying a word, she 14 a needle with a very small eye, and threaded it at her first attempt.

    When she had 15 done this, she took the thread out of the needle again and handed 16 the needle and the thread to the judge, saying, “Now it is your 17I suppose you drive a car, and that you are quite sure about your own eyesight.”

    The judge took the 18 and tried to thread it. After half a dozen tries, he had still not succeeded. The case (案例) against Mrs. Jones was19, and her record20 unbroken.