Find the coordinates of th vertex and write the equation of the axis of symmetry given the function f(x)=-x^2-3x-2.Is the vertex a maximum or a minimum?

y-k = a(x-h)^2

has vertex at (h,k).

Naturally, the max/min is at the vertex and the vertex is on the axis of symmetry.

So, all you have to do is to rearrange things a bit:

y = -x^2 - 3x - 2
y = -(x^2 + 3x) - 2
now add and subtract half of 3x, squared
y = -(x^2 + 3x + 9/4) + 9/4 - 2
y = -(x + 3/2)^2 + 1/4
y - 1/4 = -(x + 3/2)^2

Now just read off h,k