so... notice the picture below, that's P(x)
so \(\bf \qquad \qquad \textit{vertex of a parabola}\\ \quad \\
y = {{ a}}x^2{{ +b}}x{{ +c}}\qquad
\left(-\cfrac{{{ b}}}{2{{ a}}}\quad ,\quad {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\right)\)
so.. when the quantity is \(\bf -\cfrac{{{ b}}}{2{{ a}}}\) , is when the profit \(\bf {{ c}}-\cfrac{{{ b}}^2}{4{{ a}}}\) is the highest
after that, as you can see from the graph, it goes back down
