The function f(x) = 3x² + 12x +11 can be written in
vertex form as
1) f(x) = (3x + 6)² – 25
2) f(x) = 3(x + 6)^2– 25
3) f(x) = 3(x + 2)² – 1
4) f(x) = 3(x + 2)² +7

3)  f(x) = 3(x + 2)^2 - 1.

Step-by-step explanation:

f(x) = 3x² + 12x +11

f(x) = 3(x^2 + 4x) + 11        Completing the square:

f(x) =  3[(x + 2)^2 - 4] + 11

f(x) = 3(x + 2)^2 -+3*-4 + 11

f(x) = 3(x + 2)^2  - 12 + 11

f(x) = 3(x + 2)^2 - 1.

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!