Question

Which function in vertex form is equivalent to f(x) = x^2 + 6x + 3?

f(x) = (x + 3)^2 + 3
f(x) = (x + 3)^2 − 6
f(x) = (x + 6)^2 + 3
f(x) = (x + 6)^2 − 6

Answer 1

$f(x)=x^2+6x+3$

Complete the square:

$x^2+6x+a^2\implies a=\dfrac{6x}{2x}=3\implies x^2+6x+3^3$

And we have:

$f(x)=x^2+6x+3\\\\f(x)=x^2+6x+3^2-3^2+3\\\\f(x)=(x+3)^2-9+3\\\\\boxed{f(x)=(x+3)^2-6}$

Answer B.