An equation of a parabola with vertex (h,k) and which opens either upward or downward is y = A(x-h)2+k. If A>0, the parabola opens upward. If A<0, the parabola opens downward.
Since the vertex is (-6,9), we have y = A(x+6)2 + 9
Since the point (-4,13) is on the graph, 13 = A(-4+6)2 + 9
13 = 4A + 9
4A = 4 So, A = 1
Therefore, y = (x+6)2 +9.
Since the parabola opens upward (A>0), the vertex is the lowest point of the graph.
Range = set of all possible values of y = [9,∞)
Domain = set of all possible values of x = (-∞, ∞)