Identify the axis of symmetry and vertex of f (x) = - 2x2 - 2x-1.

Given the quadratic equation: f (x) = - 2x^2 - 2x - 1, the axis of symmetry can be obtained by finding the line that divides the function into two congruent or identical halves. Thus, it should pass through the vertex and is equal to the x-coordinate of the vertex.

Note that a quadratic equation in standard form: y = ax^2 + bx + c, has the vertex located at (h, k) where, h = - b/2a and k is determined by evaluating y at h. In this case, a = - 2, b = - 2, thus, h = - 0.5, k = 0.5. Thus, the vertex is located at (-0.5, 0.5) and the axis of symmetry is at x = - 0.5.