Question

How do you identify the axis of symmetry and the vertex from the equation `y=3(x+4)-22`?

Answer 1

Do you mean `y=3(x+4)^2-22`?
If so, the axis of symmetry is `x=-4`

Explanation:

Notice the parabola is symmetric about the vertical line `x=-4`
graph{y=3(x+4)^2-22 [-9.34, 1.246, -22.45, -17.157]}
In the generic formula `y=a(x-h)^2+k`, `(h,k)` is the vertex and `x=h` is the axis of symmetry.

In your example, `h` is `-4`, so the axis of symmetry is `x=-4`