Question

find the vertex and line of symmetry of f(x)=x^2+6x+3

Answer 1

(-3,-6)
line of symmetry x = -3

Answer 2

Questions?

Answer 3

wrong answer

Answer 4

it states the vertex is (3,12)

Answer 5

The x-coordinate of the vertex is -b/2a = -6/2 = -3.

y would be (-3)^2 + 6(-3) + 3 = 9 -18 + 3 = -6

With respect to you, I see no reason why the answer I gave is wrong.
And, the line of symmetry is determined by the x-coordinate of the vertex. That would be x = -3.

You did not mention that the line of symmetry is incorrect.