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What is the vertex form of #y=-3x^2 + 12x - 8#?

1 Answer

Dec 21, 2016

The vertex form of #y=-3x^2+12x-8# is #y=-3(x-2)^2+4#

Explanation:

To derive vertex form #y=a(x-h)^2+k# from general quadratic form #y=ax^2+bx+c#,
you can use completing the square

#y=-3x^2+12x-8#
#= -3 (x^2-4x+8/3)#
#= -3 (x^2-4x +(-2)^2-(-2)^2 +8/3)#
#= -3 ((x-2)^2 -4+8/3)#
#= -3 ((x-2)^2 -4/3)#
#= -3 (x-2)^2 -4#

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