用配方法把下列二次函数化成顶点式：y=ax²+bx+c

Question

用配方法把下列二次函数化成顶点式：y=ax²+bx+c

Answer 1

y=a(x²+b/a*x)+c
=a[x²+1/2*b/2a*x+(b/2a)²-(b/2a)²]+c
=a[(x+b/2a)²-b²/4a²]+c
=a(x+b/2a)²-b²/4a+c
=a(x+b/2a)²+(4ac-b²)/4a
所以顶点坐标为(-b/2a,(4ac-b²)/4a)