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问题 解答题

已知二次函数y=ax2-4x+c的图象经过点A（-1，-1）和B（3，-9）．

（1）求该二次函数的解析式；

（2）填空：该抛物线的对称轴是______；顶点坐标是______；当x=______时，y随x的增大而减小．

答案

（1）将A（-1，-1），B（3，-9）代入y=ax2-4x+c得：

a+4+c=-1
9a-12+c=-9
，

解得：

a=1
c=-6
，

则二次函数解析式为y=x2-4x-6；

（2）y=x2-4x-6=（x-2）2-10，

可得对称轴为直线x=2，顶点坐标为（2，-10），当x＜2时，y随x的增大而减小．

故答案为：直线x=2；（2，-10）；＜2．

阅读理解

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