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二次函数在某区间上的最值问题是高(会)考命题中经久不衰的“热点”,是考查学生能力和数学素养的极好素材,加之很多求代数、三角、立几、解几的最值问题,常可化归为二次函数在某区间上的最值问题来处理,越发突出了这类问题应用的广泛性和重要性,值得我们认真探研和总结。决定二次函数在某区间上的最值问题的主要因素是二次函数图象的对称轴、开口方向及所给的区间,其中二次函数图象的开口方向很容易由二次项系数的符号来确定,而对称轴与所给区间
The value of the quadratic function in a certain range is the enduring “hot spot” in the propositions of high (will) examinations. It is an excellent material for examining students’ abilities and mathematics literacy, plus many algebraic algebras, triangles, vertical numbers, and solutions. The problem of the most value of several can often be attributed to the problem of the quadratic function in the interval of the certain value, which more and more highlights the breadth and importance of the application of this type of problem. It is worth our careful exploration and summary. The main factor that determines the maximum value of the quadratic function in an interval is the axis of symmetry of the quadratic function image, the opening direction, and the given interval. The opening direction of the quadratic function image can easily be determined by the quadratic coefficient. The symbol is determined, and the axis of symmetry and the given interval