二次函数的配方法

二次函数的配方法

y = ax² + bx + c

  = a(ax²/a + bx/a) + c

  = a[x² + x(b/a)] + c

  = a{[x² + x(b/a) + ((b/a)/2)²] - ((b/a)/2)²} + c

  = a[x² + x(b/a) + (b/2a)²] + c- a(b²/4a²)

  = a[x² + x(b/a) + (b/2a)²] + c- (b²/4a)

  = a(x + (b/2a))² + c - (b²/4a)

  = a(x + (b/2a))² +(4ac/4a) - (b²/4a)

  = a(x + (b/2a))² +(4ac - b²)/4a

对 称 轴:  x + (b/2a) = 0 , 即 x = -(b/2a)

顶点坐标:  (-(b/2a) , (4ac - b²)/4a)