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题目已知函数覼(x)=-x2+ax+b(a,b∈R)的值域为(-∞,0],若关于x的不等式覼(x)>c-1的解集为(m-4,m+1),则实数c的值为______.此题为上海市长宁区2012~2013学年第一学期期末试卷高三数学理科第13题,是一道利用二次函数、二次不等式知识解决新问题的把关题.由于式子含有多个字母参数,虽然很多同学知道应该用函数与不等式的知识,但应如何消去字母参数求实数c的值?笔者经过研究发现,可以从多方位思考本题.笔者就从“解、悟、变”来谈谈自己的思悟,以期抛砖引玉.
Problem It is known that the range of the function 覼 (x) = - x2 + ax + b (a, b∈R) is (-∞, 0]. If the inequality 覼 (x)> c- (m-4, m + 1), then the real value of c is ______ .This is the Shanghai Changning District 2012 ~ 2013 academic year the first semester of the third grade senior high school mathematics science 13 questions, is to use a quadratic function, two Although the formula contains many alphabetic parameters, although many students know that we should use the knowledge of function and inequality, how to eliminate the value of the real number c of the letter parameter? The author has found through research that it can be obtained from Multidimensional thinking of the problem. The author from the “solution, enlightenment, change” to talk about their own enlightenment, with a view to start a discussion.