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)#