二次函数是一个重要的初等函数,它与一元二次方程、一元二次不等式密切联系,函数与方程的思想、数形结合的思想、分类讨论的思想、等价转化的思想在这里得到充分的体现.本文着重分析三类问题:区间上的二次函数的单调性;区间上的二次函数的最值与值域;区间上的二次函数的恒正与恒负. The quadratic function is an important elementary function. It is closely related to the unary quadratic equation and the unary quadratic inequalities. The idea of ​​the function and the equation, the idea of ​​the combination of numbers and shapes, the idea of ​​classification and discussion, and the idea of ​​equivalent transformation are fully understood here. This paper focuses on three types of problems: the monotonicity of the quadratic function in the interval; the maximum and the range of the quadratic function in the interval; the constant positive and negative of the quadratic function in the interval.