形如 f(x)=ax~3+bx~2+cx+d(a≠0)的函数,叫做三次函数.由于三次函数的导函数是二次函数,而二次函数是高中数学中的重要内容,所以三次函数的问题,已经成为高考命题的一个新的热点和亮点,尤其是文科数学更是如此.我们可以采用类比的方法,结合几何画板软件,较为深人地研究三次函数的图象与性质,以及三次方程的解的个数的问题. A function of the form f(x)=ax~3+bx~2+cx+d(a≠0) is called a cubic function. Since the derivative function of a cubic function is a quadratic function, the quadratic function is used in high school mathematics. The important content, so the problem of the cubic function has become a new hot spot and bright spot of the college entrance examination proposition, especially the liberal arts mathematics. We can use the analogy method, combined with the geometry drawing board software, to study the graph of the cubic function more deeply. Image and nature, and the number of solutions to the cubic equation.