the C(x) equation is a parabola with a squared "x" and a positive leading term coefficient, meaning, is a vertical parabola and it opens upwards
the lowest point, or lowest cost value, it reaches, is the U-turn point, or vertex
[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\
\begin{array}{llccll}
y = &{{ 1}}x^2&{{ -320}}x&{{ +40052}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)[/tex]
so, the lowest cost is at [tex]\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}[/tex]