How to find the vertex of f(x)=x^2-4

The number +2 represents h and -4 represents k in the general form given above. To find the vertex, simply change the signs in front of h and k to the OPPOSITE value and you will find the vertex of the parabola.
The maximum value is the vertex. So, the maximum value is the point (-2, 4).
There is no minimum value for this function because the parabola faces downward.
You said line of symmetry, right? I am sure that you meant to type axis of symmetry.
What is the axis of symmetry? The axis of symmetry is the line that CUTS the parabola exactly in two equals parts at the vertex. It is line that goes through the vertex dividing the parabola into two EQUAL pictures.
The axis of symmetry is the equation x = h.
Do you know the value of h? You sure do. We want it above, right?
The axis of symmetry is the value of h as given in the vertex point or simply x = -2. That is your axis of symmetry.

To find the vertex of a parboil a equation, you can complete the square, take two of the zero x values and divide by 2 because the parbola is between these two x root values F(x) = x^2-4, however this function is a difference of squares F(x) = (x -2)(x+2) Which means when x = -2,2 we have (-2+2)/2 = 0 = x. And solving for y gives us (-2)(2)= -4. So, out vertex is point (0,-4)