Solve for: p(x)=-0.01x^2+62x-12000

Expression: $p\left( x \right)=-0.01{x}^{2}+62x-12000$

Identify the coefficients $a$ and $b$ of the quadratic function

$\begin{array} { l }a=-0.01,& b=62\end{array}$

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 $x$


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 $\left( 3100, -0.01 \times {3100}^{2}+180200\right)$

$\begin{align*}&\left( 3100, -0.01 \times {3100}^{2}+180200\right) \\&\left( 3100, -\frac{ 1 }{ 100 } \times {3100}^{2}+180200\right)\end{align*}$