What is the vertex form of #y=-9x^2 +12x - 18 #?

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Answer 1 · 2015-12-26T01:53:47

Below is the proof (a completion of square)

#y = -9x^2 + 12x - 18#

#y = -9(x^2 - 12/9x) - 18#

#y = -9(x^2 - 12/9x + #_ - _ ) - 18#

#_ = ((-12/9) / 2)^2#

#_ = 4/9#

#y = -9(x^2 - 12/9x + 4/9) - 4/9(-9) - 18#

#y= -9(x - 2/3)^2 - 14#

So, #y = -9x^2 + 12x - 18# is equal to #y = -9(x - 2/3)^2 - 14#

Hopefully that explanation helped!