check the picture below.
[tex]\bf \textit{ vertex of a vertical parabola, using coefficients}\\\\
\begin{array}{lccclll}
R(p) = &{{ -10}}p^2&{{ +130}}p&{{ +0}}\\
&\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{130}{2(-10)}~~,~~0-\cfrac{130^2}{4(-10)} \right)\implies
\left( \cfrac{13}{2}~~,~~\cfrac{4225}{10} \right)
\\\\\\
\left( \stackrel{price}{6\frac{1}{2}}~~,~~\stackrel{revenue}{422\frac{1}{2}} \right)[/tex]
