下列的函数用配方法化为顶点式,需要过程,非常感谢!
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发布时间：2023-08-20 00:44
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热心网友
时间：2024-10-22 16:49
= (1/3)(x^2 - 15x + 21)
= (1/3)[x^2 - 2*(15/2) + (15/2)^2 + 21 - (15/2)^2]
= (1/3)[ (x -15/2)^2 - 141/4]
= (1/3)(x - 15/2)^2 - 47/4
y = (- 4/3)x^2 - 8x - 13
= (-4/3)(x^2 + 6x +39/4)
= ( -4/3)[ x^2 + 2*3x + 3^2 + 39/4 - 3^2]
= (-4/3)[ (x + 3)^2 + 3/4]
= (-4/3)(x + 3)^2 - 1
y = (3/2)x^2 - 2x + 6
= (3/2)[x^2 - (4/3)x + 4]
= (3/2)[ x^2 - 2*(2/3)x + (2/3)^2 + 4 - (2/3)^2]
= (3/2)[ (x - 2/3)^2 + 32/9]
= (3/2)(x-2/3)^2 + 16/3
y = -x^2 + 2x - 1
= -(x^2 - 2x + 1)
= -(x - 1)^2
y = (-3/4)x^2 + 2x + 7/2
= (-3/4)[x^2 - (8/3)x - 14/3]
=(-3/4)[ x^2 - 2*(4/3)x + (4/3)^2 - 14/3 - (4/3)^2]
= (-3/4)[(x - 4/3)^2 -58/9]
= (-3/4)(x- 4/3)^2 + 29/6
y = -2x^2 + 20x
= -2(x^2 - 10x)
= -2(x^2 - 2*5x + 5^2 - 5^2)
= -2(x - 5)^2 + 50
y = -2x^2 + 20x + 1
= -2(x^2 - 10x - 1/2)
= -2(x^2 - 2*5x + 5^2 - 1/2 - 5^2)
= -2(x-5)^2 + 51/2
y = -x^2 + 6x - 7
= -(x^2 - 6x + 7)
= -(x^2 - 2*3x + 3^2 + 7 - 3^2)
= -(x-3)^2 + 2
y = (-1/2)x^2 + x - 5/2
= (-1/2)[x^2 - 2x + 5]
= (-1/2)[ x^2 -2x + 1 + 4]
= (-1/2)(x-1)^2 - 2
y = 4x^2 - 2x + 5
= 4(x^2 -1/2x + 5/4)
= 4(x^2 - 2*(1/4)x + (1/4)^2 + 5/4 - 1/16]
= 4(x - 1/4)^2 + 19/4
另外，你说到的二次项系数归一化时，可以采用以下方法
y = ax^2 + bx + c
= a[x^2 + (b/a)x + (c/a)]
即：各项同时提出二次项系数a
