The given function is a quadratic function in the form y = ax^2 + bx + c, where a = -1, b = -2, and c = 3.

To graph the function, we can first find the vertex, y-intercept, and x-intercept(s) of the function.

Vertex:
The x-coordinate of the vertex of a quadratic function in the form y = ax^2 + bx + c is given by x = -b/2a.
In this case, x = -(-2)/(2*(-1)) = 1.
Substitute x = 1 into the function to find the y-coordinate of the vertex: y = -(1)^2 - 2(1) + 3 = -1 - 2 + 3 = 0.
Therefore, the vertex of the function is at (1, 0).

Y-intercept:
To find the y-intercept, substitute x = 0 into the function: y = -(0)^2 - 2(0) + 3 = 3.
Therefore, the y-intercept of the function is at (0, 3).

X-intercept(s):
To find the x-intercept(s), set y = 0 and solve for x:
0 = -x^2 - 2x + 3
0 = x^2 + 2x - 3
0 = (x + 3)(x - 1)
x = -3 or x = 1
Therefore, the x-intercepts of the function are at (-3, 0) and (1, 0).

Now we can plot these points on a graph and sketch the graph of the function y = -x^2 - 2x + 3 passing through these points.