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在函数的教学中,经常遇到求满足某式恒成立时的参数取值范围的问题,随着对代数课程学习的深入,这类题目有着越来越多的不同的解法。而对一个有代表性的例题,通过一题多解,总结一类问题的各种解法之间的内在联系,将有助于学生系统地掌握数学问题的各种思路和方法。本文通过解析当一个二次函数大于等于零恒成立时,求其参数取值范围的例题来说明一题多解能将多种知识综合起来,从而增强学生对数学基础知识的掌握。
In the teaching of functions, we often encounter the problem of seeking the range of parameters when a certain constant is established. With the deepening of the study of algebra, there are more and more different solutions to these problems. And for a representative example, through the multi-solution of one question, summarizing the internal relations among the various solutions of a kind of question, it will help students to systematically grasp the various ideas and methods of mathematical problems. In this paper, by analyzing a case when the value of a quadratic function is greater than or equal to zero, we can find a range of parameter values to illustrate that a problem with multiple solutions can combine a variety of knowledge to enhance students’ understanding of the basic knowledge of mathematics.