怎样用配方法把二次函数一般式配成顶点式

2025-03-25 03:13:41
推荐回答(2个)
回答1:

y=ax^2+bx+c
=a(x^2+b/ax+c/a)
=a[x^2+b/ax+(b/2a)^2-(b/2a)^2+c/a]
=a[(x+b/2a)^2-b^2/4a^2+c/a]
=a[(x+b/2a)^2-b^2/4a^2+4ac/4a^2]
=a[(x+b/2a)^2+(4ac-b^2)/4a^2]
=a(x+b/2a)^2+(4ac-b^2)/4a

回答2:

y=ax²+bx+c. y=a(x-b/2a)²+(4ac-b²)/4a