二次函数最值问题解题方法的研究

二次函数最值问题解题方法的研究摘要二次函数是数学中极其重要的内容之一，对于初、高中的数学学习来说有一个承前启后的作用。中考中二次函数最值问题更是一个常考的考点。该考点涉及广泛，灵活多变，在三角形等几何领域有丰富的应用。随着新课标的改革，对学生掌握知识的程度和综合能力要求也相应提高，中考考查的知识相对综合。通过研究有关二次函数最值问题的所涉及到的基础知识、相关的题型以及翻阅相关文献来分析和研究二次函数最值问题的解题方法。本文共研究和探讨了四种解题方法：利用基础知识解题、构建数学模型解题、通过分类讨论解题以及联系实际情况解题，并且提供了相应的示例和小结，结论是在解题的方法中关键是掌握二次函数的基础知识并且需要学生灵活应用。解题时最重要的是要注意寻找题干所给变量之间的关系，以及研究自变量的取值范围。这些需要学生增强数学抽象和建模的能力。最后提出了一些教学建议：老师加强基础知识的教学、注重解题方法的教授、培养学生的数学逻辑和抽象思维能力、增加实际应用的教学：学生要打好基础，认真审题，注意挖掘题目所给隐藏条件，需要掌握各个不同的题型的方法但是不可照搬套路。关键词：二次函数：解题方法：最值问题AbstractQuadratic function is one of the most important contents in mathematics,which plays animportant role in the study of mathematics in junior and senior high schools.In the middleschool entrance examination,the quadratic function maximum value problem is a commontest point.The test site involves a wide range of flexible and changeable,and has richapplications in geometry fields such as triangles.With the reform of the new curriculumstandard,the requirements of students'knowledge and comprehensive ability are alsoimproved accordingly,and the knowledge examined in the senior high school examination isrelatively comprehensive.This paper analyzes and studies the solution of quadratic functionmaximum value problem by studying the basic knowledge,related question types andreviewing related literature.This paper studies and discusses four problem-solving methods:solving problems withbasic knowledge,building mathematical models,solving problems through classification anddiscussion,and solving problems in connection with the actual situation,and providescorresponding examples and summaries.The conclusion is that the key to solving problems isto master the basic knowledge of quadratic functions and students need to apply them flexibly.When solving the problem,the most important thing is to find the relationship between thevariables given by the problem stem and study the value range of independent variables.These require students to enhance their ability in mathematical abstraction and modeling.Finally,some teaching suggestions are put forward:teachers should strengthen the teaching ofbasic knowledge,pay attention to the teaching of problem-solving methods,train students'ability of mathematical logic and abstract thinking,and increase the teaching of practicalapplication;Students should lay a good foundation,carefully examine the questions,payattention to excavating the hidden conditions given by the questions,need to master themethods of different types of questions,but can not copy the routine.Key words:Quadratic function;method of problem solving;maximum problem目录第1章引言.....1.1研究内容…11.2研究意义.1第2章二次函数最值问题简述........22.1初中二次函数的最值问题.22.2初中二次函数最值问题常见题型3第3章二次函数最值问题解题方法3.1利用基础知识解题…43.2构建数学模型解题…53.3通过分类讨论解题….63.4联系实际情况解题.…7第4章总结及反思….84.1总结及教学建议…84.2不足和展望..9参考文献..…….11致谢.…….12