The easiest way to write this is in vertex form, as you are already given the vertex: (1,-3)
Vertex form: Y = a(x-h)^2+k
Plugging in the vertex into (h,k) you get:
Y = a(x-1)^2 - 3
In order to find a, you need to plug in another point into x and y (that's not the vertex, or else you'll get all real #'s).
Plug in (0,-4) since you are also given that on the graph.
-4 = a(0-1)^2 - 3
-1 = a
a = -1
For your final answer you get:
