How do you write the quadratic in vertex form given $f(x)=x^2 + 6x + 12$ ?

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Answer 1 · 2015-05-12T20:36:47

$f(x) = x^2 + 6x + 12$

$= (x+3)^2 - 9 + 12$

$= (x+3)^2 + 3$

In general, $ax^2 + bx+ c$ can be written in vertex form as

$a(x+(b/(2a)))^2+(c-b^2/(4a))$

In the case $a=1$ , this simplifies to

$x^2+bx+c = (x+b/2)^2 + (c - b^2/4)$

How do you write the quadratic in vertex form given f(x)=x^2 + 6x + 12f(x)=x^2 + 6x + 12?