题目内容

某校学生社团心理学研究小组在对学生上课注意力集中情况的调查研究中，发现其注意力指数与听课时间之间的关系满足如图所示的曲线。当时，曲线是二次函数图象的一部分，其中对称轴为；当时，曲线是函数图象的一部分。根据专家研究，当注意力指数大于或等于80时听课效果最佳．
（1）试求的函数关系式；
（2）老师在什么时间段内安排核心内容能使学生听课效果最佳？请说明理由．
（1）
（2）解析:
本试题主要考查了函数的图像与解析式的关系，以及简单的运用。
解：（1）时，设 
将代入得c=-1/4
时，   ……3分
时，将(14,81)代入，得a=1/3        ……6分
∴   。。。。。。。。．   8分
（2）时，解得，
∴                                               ……11分
时，解得， ∴， ……13分
∴，                                           ………14分
答：老师在内安排核心内容能使学生听课效果最佳
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