What is the vertex form of #y=(x-6)(x-3)#?

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Answer 1 · 2016-04-04T10:06:43

#color(blue)(y=(x-9/2)^2 - 9/4)#

given:#y=color(blue)( (x-6)color(brown)((x-3)))#

Multiply out the brackets giving

#y=color(brown)(color(blue)(x)(x-3)color(blue)(-6)(x-3))#

#y=x^2-3x-6x+18#

#y=x^2-9x+18#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Compare to standard form #y=ax^2+bx+c#

Where #a=1" ; "b=-9" ; "c=18#

The standard for the vertex form of this equation is:

#y=a(x+b/(2a))^2+c - [ (b/2)^2]#

So for your equation we have

#y=(x-9/2)^2+18 - [ - 81/4]#

#color(blue)(y=(x-9/2)^2 - 9/4)#