What value of $x$ will give the minimum value of $2x^2 - 12x + 3$?
I notice that this is a quadratic function, and I recall that the minimum or maximum value of a quadratic function occurs at the vertex of its parabola. I also remember that the x-coordinate of the vertex is given by the formula $-\frac{b}{2a}$, where $a$ and $b$ are the coefficients of $x^2$ and $x$ respectively. In this case, $a = 2$ and $b = -12$, so the x-coordinate of the vertex is $-\frac{-12}{2(2)} = 3$. This means that the minimum value of the function occurs when $x = 3$. 