配套习题- 二次函数压轴题——正方形问题 -【青果学院】

1/5单选题

难度：

1.边长为1的正方形OABC的顶点A在x正半轴上，点C在y正半轴上，将正方形OABC绕顶点O顺时针旋转75°，如图所示，使点B恰好落在函数y=ax²（a＜0）的图象上，则a的值为（　　）

A
B	1
C
D

正确答案：RA==

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

2/5单选题

难度：

2.如图，在平面直角坐标系中，二次函数y=ax²+mc（a≠0）的图象经过正方形ABOC的三个顶点，且ac=-2，则m的值为（　　）

A	1
B	-1
C	2
D	-2

正确答案：QQ==

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

3/5单选题

难度：

3.如图，在平面直角坐标系中，二次函数y=ax²+c（a≠0）的图象过边长为1的正方形ABOC的三个顶点A、B、C，则ac的值为（　　）

A	-2
B	-1
C
D

正确答案：QQ==

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

4/5单选题

难度：

4.如图，抛物线y=-

+2bx+c（b＞0）与y轴交于点C，点P为抛物线顶点，分别作点P，C关于原点O的对称点P′，C′，顺次连接四点得四边形PC P′C′. 四边形PCP′C′为正方形时，符合条件的b，c的值分别为（）

A	c=-1，b=1
B	c=1，b=1
C	c=1，b=-1
D	不能确定

正确答案：QQ==

6Kej77ya5b2T5Zub6L655b2iUENQ4oCyQ+KAsuiDveaIkOS4uuato+aWueW9ouaXtu+8jFBQ4oCy4oqlQ0PigLLkuJRPUD1PQzxicj7mraTml7bngrlQ5b+F5ZyoeOi9tOS4iu+8jDxicj7iiLQ8aW1nIHdpZHRoPTg5IGhlaWdodD00MiBzcmM9Imh0dHBzOi8vcDIucWluZ2d1by5jb20vRzEvTTAwLzc1L0I5L3JCQUNGRlBrY1FXQkpteXdBQUFDb2c1YUVodzMwMi5wbmciPj1jK2I8c3VwPjI8L3N1cD49MOKRoO+8jDxicj7iiLVPUD1PQ++8jOeCuUPlv4XlnKh56L2055qE6LSf5Y2K6L205LiK77yM4oi0Yj0tY+KRoe+8jDxicj7nlLHikaDikaHlvpfvvIxjPTDvvIjoiI3ljrvvvInvvIxjPS0x77yMPGJyPuKItGI9MS4gPGJyPuaVhemAiUHjgII=

5/5单选题

难度：

5.已知：抛物线m：y=a

+b（ab＜0）的顶点为P，与x轴的交点为A，B（点A在点B的左侧）. 若将抛物线m沿x轴翻折180°得抛物线n，抛物线n的顶点为Q，则以A，P，B，Q为顶点的四边形为正方形a，b满足的关系式为（）

A	ab=1
B	ab=2
C	ab=-1
D	ab=-2

正确答案：Qw==

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