I forgot how to complete the square, how would I convert 3x^2 + 12x + 11 to vertex form?

Question

phi · Answer

write it as
$$ (3x^2+12x) + 11 \ 3(x^2 + 4x) +11$$
now inside the parens add and subtract (4/2)^2

xmissalycatx · Answer

Hey there! :)

Here is an image to help you better understand of to CTS.

onepieceftw · Answer

Okay @phi , then what? This is when I factor out the trinomial x^2+4x+4? then distribute the 3

phi · Answer

you should have this:
$$ y = 3x^2 + 12x + 11 \
y= 3(x^2 +4x) + 11$$
then we find (4/2)^2 = 2^2 =4
we add and subtract 4:  +4-4  (which is zero, so  the value is not changed)
$$ y= 3(x^2 +4x+4  -4) + 11$$
now group the first three terms which form a perfect square 
$$ x^2 +4x+4 = (x+2)^2 $$ so you have
$$ y= 3( (x+2)^2  -4) + 11$$

phi · Answer

now distribute the 3 and combine the numbers

onepieceftw · Answer

So I have $$y = 3(x+2)^2-1$$

phi · Answer

yes, and if we write it to match
y = a(x-h)^2 + k:
$$ y= 3(x- -2)^2 -1$$
the vertex is -2, -1

onepieceftw · Answer

Thanks, really appreciate your help!