If it is y=x^2 +6x+1 follow this way because if your equation is not for a real function!!!
At first we should find the vertex of parabola: vertex s y = -b/2a ==>-6/2=-3
then find the max or min of the parabola:
Y=-8
so finally we know y=ax^2 + bx + c =(x-h)^2 +k
if vertex is (h,k):
Y=(x+3)^2 -8
Ok?