Finding Minimum Value of Function g(x)

Consider the function $f(x) = 2x^2 - 4x + 1$. Determine the value of $x$ at which the function $g(x) = f(x) - 3$ reaches its minimum value. Provide your answer based on the minimum point of the function $g(x)$.

Recall that the vertex of a quadratic function of the form $ax^2 + bx + c$ occurs at $x = -\frac{b}{2a}$. Use this concept to find the minimum value of $g(x)$.