Since you need the vertex, and knowing the vertex will tell you the axis of symmetry, it is convenient to put the equation in vertex form. .. -x^2 -4x +1 .. = -(x^2 +4x) +1 .. = -(x^2 +4x +(4/2)^2) +1 -(-(4/2)^2) . . . . complete the square .. = -(x +2)^2 +5
The vertex is (-2, 5). The axis of symmetry is x = -2.