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含有参数的一元二次不等式恒成立问题,因其需要一元二次函数、一元二次方程和一元二次不等式等知识以及相互之间的转化和联系,思维容量大、综合性强,使之成为学生在学习函数及不等式等知识的难点。同时,这类问题的解决,又往往需要运用数形结合法:构造二次函数并运用二次函数的图象和性质来进行求解。而含参问题又往往要分类讨论,使学生求解更容易出现失误。所以这类问题学生解决起来困难较多且有效性很低,隔一段时间后同样问题反复出现。
The univariate quadratic inequalities with parameters are constancy problems because they require such knowledge as univariate quadratic functions, univariate quadratic equations and univariate quadratic inequalities, as well as transformation and connection with each other, with large thinking capacity and comprehensiveness, making them Students are having difficulty learning about functions and inequalities. At the same time, the solution of such problems often requires the use of the method of combination of numbers: the construction of quadratic functions and the use of quadratic function of the image and the nature of the solution. The problem of containing parameters is often classified discussion, so that students solve more prone to mistakes. Therefore, students with such problems are more difficult to solve and have low effectiveness. The same problems recur after a period of time.