Question

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

Answer 1

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

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.