Question

What is the axis of symmetry of the graph of `y=-(x+3)^2-6`?

Answer 1

If you complete the square, as was done in this case, it's not hard.
It's also easy to find the vertex.

`(x+3)` means that the parabola is displaced `3` to the left as compared to the standard-parabola `y=x^2`
(because `x=-3` would make `(x+3)=0`)

[It is also displaced `6` down, and the minus in front of the square means it's upside down, but that has no influence on the symmetry-axis, ]

So the axis of symmetry lies at `x=-3`
And the vertex is `(-3,-6)`
graph{-(x+3)^2-6 [-16.77, 15.27, -14.97, 1.05]}