题目内容
已知二次函数的图象以A(
,
)为顶点,且过B(
,
)
(1)求该函数的关系式;
(2)求该函数图象与坐标轴的交点坐标;
(3)将该函数图象向右平移,当图象经过原点时,A、B两点随图象移至点
、
,
求
的面积。


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
(1)求该函数的关系式;
(2)求该函数图象与坐标轴的交点坐标;
(3)将该函数图象向右平移,当图象经过原点时,A、B两点随图象移至点


求

(1)函数关系式为
或
(2)与
轴的交点坐标为(-3,0),(1,0);
与
轴的交点坐标为(0,3).
(3)
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
(2)与

与

(3)

试题分析:解:(1)由题意可设该函数关系式

则


∴所求函数关系式为


(2)对于



当


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
∴与

与

(3)因为函数图像向右平移3个单位后过原点.
所以平移后的点A′(2,4),B′(5,-5).
∴

点评:本题难度中等,主要考查学生对二次函数知识点的掌握。要求数量掌握其各特殊点坐标规律。
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