remember that quadratic equation y = ax^2+bx + c represents a parabola.
we can convert it to what is called a Vertex form y = a(x-h)^2 + k and then the point (h,k) is the vertex of the parabola and x= h is the axis of the parabola.
in this case we have
y = x^2 + 2x = x^2 + 2x + 1 -1= ( x+1)^2 -1
compare what is h and k and you have the coordinates of the vertex