如何快速判断二次函数单调性

2025-04-07 01:36:15
推荐回答(3个)
回答1:

具体分类如下:

①当a大于0时,因为抛物线开口朝上。

所以x小于-b/2a时,函数单调减,(就是在对称轴x=-b/2a左边)。

x大于-b/2a时,函数单调增。

②当a小于0时,抛物线开口朝下。

x小于-b/2a时,函数单调增,(就是在对称轴x=-b/2a左边)。

x大于-b/2a时,函数单调减。

二次函数

二次函数(quadratic function)的基本表示形式为y=ax²+bx+c(a≠0)。二次函数最高次必须为二次,二次函数的图像是一条对称轴与y轴平行或重合于y轴的抛物线。

二次函数表达式为y=ax²+bx+c(且a≠0),它的定义是一个二次多项式(或单项式)。

如果令y值等于零,则可得一个二次方程。该方程的解称为方程的根或函数的零点。

回答2:

具体分类如下:
①当a大于0时,因为抛物线开口朝上,
所以x小于-b/2a时,函数单调减,(就是在 对称轴x=-b/2a 左边),
x大于-b/2a时,函数单调增
②当a小于0时,抛物线开口朝下,
x小于-b/2a时,函数单调增,(就是在 对称轴x=-b/2a 左边),
x大于-b/2a时,函数单调减

回答3:

具体分类如下:
①当a大于0时,因为抛物线开口朝上,
所以x小于-b/2a时,函数单调减,(就是在 对称轴x=-b/2a 左边),
x大于-b/2a时,函数单调增
②当a小于0时,抛物线开口朝下,
x小于-b/2a时,函数单调增,(就是在 对称轴x=-b/2a 左边),
x大于-b/2a时,函数单调减

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