$\begin{array} { l }a=-0.01,& b=62\end{array}$
Find the $x$-coordinate of the vertex by substituting $a=-0.01$ and $b=62$ into $x=-\frac{ b }{ 2a }$$x=-\frac{ 62 }{ 2 \times \left( -0.01 \right) }$
Solve the equation for $x$$x=3100$
Find the $y$-coordinate of the vertex by evaluating the function for $x=3100$$\begin{array} { l }p\left( x \right)=-0.01{x}^{2}+62x-12000,& x=3100\end{array}$
Calculate the function value for $x=3100$$p\left( 3100 \right)=-0.01 \times {3100}^{2}+180200$
The vertex of the graph of the quadratic function is at $\left( 3100, -0.01 \times {3100}^{2}+180200\right)$$\begin{align*}&\left( 3100, -0.01 \times {3100}^{2}+180200\right) \\&\left( 3100, -\frac{ 1 }{ 100 } \times {3100}^{2}+180200\right)\end{align*}$