在中学数学教材中对二次函数的研究是非常透彻的,包括它在单调性和对称性方面表现出的性态.但三次函数仅仅是通过导数去研究了它的单调性,而对于对称性教材只字未提,对三次函数对称性的研究更有利于把握三次函数图象的性态.针对三次函数对二次函数的依赖性,笔者通过类比的方法谈谈三次函数对称性的探索过程.首先,让我们一起看看二次函数对称性的探究过程.先看:f(x)=ax2(a≠0)关于y轴对称(这是因为它是偶 The research on the quadratic function in the mathematics textbook of middle school is very thorough, including its monotonicity and symmetry.However, the cubic function only studies its monotony through the derivative, but for the symmetry The textbook is silent, the study of the symmetry of the cubic function is more conducive to grasp the state of the cubic function image.For the dependence of the cubic function on the quadratic function, the author talks about the exploration process of the symmetry of the cubic function by analogy Let us first look at the process of exploring the symmetry of quadratic functions. Let us first look at: f (x) = ax2 (a ≠ 0) Symmetry about the y axis (this is because it is even