Question

What is the axis of symmetry and vertex for the graph `y = x^2 − 4`?

Answer 1

Axis of symmetry is `0`
Vertex is `-4`

Explanation:

`y = x^2 - 4` is just `y = x^2` translated 4 units in the -y direction.

The axis of symmetry of `y = x^2` is 0 so there will be no change in the axis of symmetry when this is translated in the y direction.

When a quadratic equation is arranged in the form `a( x - h )^2 + k`

`a` is the coefficient of `x^2` , `h` is the axis of symmetry and `k` is the maximum or minimum value of the function( this is also the y coordinate of the vertex).

From example;

`y = x^2 -4` would be `( x - 0 )^2 - 4`

See graph for translation: