the cost equation is a parabolic graph, whose "lowest value" is at its vertex, it is up and goes down down down, reaches the U-turn and then goes up up up again.
[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\
\begin{array}{llll}
y = &{{ 1}}x^2&{{ -10}}x&{{ +43}}\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)
\\\\\\
\left( -\cfrac{(-10)}{2(1)}~~,~~43-\cfrac{(-10)^2}{4(1)} \right)\implies (\stackrel{\textit{items to produce}}{5}~~,~~\stackrel{\textit{production cost}}{18})[/tex]
