Question

What is the axis of symmetry and vertex for the graph `y = x^2 - 2`?

Answer 1

axis of symmetry is x = 0
vertex (0,-2)

Explanation:

The graph of `y = x^2 " is symmetrical about the y-axis"`
and has it's vertex at the origin (0,0) as shown below.
graph{x^2 [-10, 10, -5, 5]}
The graph of `y = x^2 - 2 " is the graph of " y = x^2`

but translated by `((0),(-2)) " moved 2 units down vertically"`

It is still symmetrical about the y-axis

hence axis of symmetry is x = 0 .

and vertex at (0,-2) as shown on graph.
graph{x^2-2 [-10, 10, -5, 5]}