配套习题- 二次函数压轴题——梯形问题 -【青果学院】

1/5单选题

难度：

1.如图，已知二次函数y=-x²+2mx的图象经过点B（1，2），与x轴的另一个交点为A，点B关于抛物线对称轴的对称点为C，过点B作直线BM⊥x轴垂足为点M. 在直线BM上有点P（1，

），连结CP和CA，在坐标轴上以A、C、P、E为顶点的四边形为直角梯形，则满足条件的点E的坐标为（）

A	E₁（，0）、E₂（0，-）
B	E₁（，0）、E₂（0，-）
C	E₁（2，0）、E₂（0，-）
D	E₁（，0）、E₂（0，-）

正确答案：QQ==

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

2/5单选题

难度：

2.如图，已知抛物线y=-x²+4x（x≥0）与抛物线y=

x²相交于点O和点A，现有一条动直线x=t（0＜t＜3）与它们分别交于点B和点C. 当直线运动到何位置即t为（）时，四边形OCAB为梯形

A	或
B	或
C	或
D	或

正确答案：RA==

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

3/5单选题

难度：

3.如图，二次函数y=

x²-2x+2，过点M（2，0），直线AB与该二次函数的图象交于A（0，2）、B（6，8）两点. P为线段AB上一动点（A、B两端点除外），过P作x轴的垂线与二次函数的图象交于点Q，线段AB上存在一点P，使四边形PQMA为梯形，请求出点P的坐标（）

A	（2，4）
B	（4，6）
C	（3，5）
D	（1，3）

正确答案：Qg==

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

4/5单选题

难度：

4.如图，抛物线y=a（x-1）²+4与x轴交于点A，B，与y轴交于点C，过点C作CD∥x轴交抛物线的对称轴于点D，连接BD，已知点A的坐标为（-1，0）求梯形COBD的面积（）.

A	4
B	5
C	6
D	7

正确答案：Qw==

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

5/5单选题

难度：

5.如图，已知抛物线y=

x²-

x-3与x轴的交点为A、D（A在D的右侧），与y轴的交点为C. 设点C关于抛物线对称轴的对称点为B，在抛物线上存在点P，使得以A、B、C、P四点为顶点的四边形为梯形,则此时点P的坐标为（）

A	（-2，0）或（6，6）
B	（-2，0）或（3，6）
C	（1，）或（6，-6）
D	（-1，）或（3，6）

正确答案：QQ==

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