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

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

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

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