Question

How do you graph and label the vertex and axis of symmetry of `y=-2(x+1)^2-4`?

Answer 1

Vertex: `V(-1,-4)`
Axis of symmetry: `x=-1`

Explanation:

graph{y=-2(x+1)^2-4 [-10, 10, -5, 5]}
In `y=ax^2`, the vertex is `V(0,0)`.
If you shift the graph `b` to the left and `c` up, you get `y=a(x-b)^2+c`. The vertex is shifts along with the rest of the graph, so it becomes `V(b,c)`. In this case `b=-1` and `c=-4`, so `V(-1,-4)`.

The axis of symmetry is the vertical line that goes trough the vertex, so `x=b`. Or in this case: `x=-1`.