二次函数怎么配方?(例:y=3x²+2x)

问题描述:

二次函数怎么配方?(例:y=3x²+2x)

例如:y=3x²+2x
先提取二次系数3可得:
y=3(x²+ 2x/3)
=3【x²+ 2*x*(1/3) + (1/3)² -(1/3)²]
=3【(x+ 1/3)²- (1/9)]
=3(x+ 1/3)²- (1/3)
一般的:
形如y=ax²+bx+c经过配方后可得:
y=a*[x+ b/(2a)]²+ (4ac-b²)/4a