To find the minimum value of the function y = x^2 - 2x - 3, we can start by completing the square.
First, let's add and subtract the value (-2/2)^2 = 1 to the expression inside the parentheses:
y = x^2 - 2x + 1 - 1 - 3
Next, we can group the first three terms and write them as a perfect square:
y = (x - 1)^2 - 4
Now we can see that the minimum value of the function occurs when (x - 1)^2 is zero, which happens when x = 1. Therefore, the minimum value of the function is y = -4, which occurs when x = 1.
So the answer is -4, and we can explain it by completing the square to find the vertex of the parabolic function. The vertex of the parabola y = x^2 - 2x - 3 is (1, -4), and the minimum value of the function occurs at this point.