The function \(y = -3 - 2x + x^2\) is a quadratic function, which means its graph is a parabola.

The minimum value of a quadratic function is attained at its vertex. The x-coordinate of the vertex of a parabola in the form \(y = ax^2 + bx + c\) is given by the formula \(-\frac{b}{2a}\).

In this case, we have `a = 1`, `b = -2`, and `c = -3`, so the x-coordinate of the vertex is \(-\frac{-2}{2(1)} = 1\). Therefore, the function \(y = -3 - 2x + x^2\) attains its minimum value at `x = 1`.