In my opinion of course it's impossible to locate complex roots on a functional graph. But you can find complex roots by performing some calculations on some specfic points on the parabola. There are probably many methods and this one requires you to locate the vertex of the parabola. Let and the discriminant is less than zero.
Let the coordinate of the vertex be , then by doing some calculations:
Now you can see that the quadratic formula can be rewritten in terms of the coordinates of the vertex, which is easy to derive:
(Actually this generates all the roots.)