What is the vertex form of #y = 6x^2 - 24x + 16#?

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Answer 1 · 2018-07-08T17:49:44

#y=6(x-2)^2-8#

We have

#y=6x^2-24x+16#
and this is

#y=6(x^2-4x+16/6)#
#y=6(x^2-4x+8/3)#
now we complete the square

#y=6(x^2-4x+4+8/3-4)#

we use that

#x^2-4x+4=(x-2)^2#
and

#8/3-4=8/3-12/3=-4/3#

so we get

#y=6(x-2)^2-6*4/3#

the result is given by

#y=6(x-2)^2-8#
and this is the vertex form