Question 25161d0e

An auditorium has seats for $\mathrm{1,800}$ people. Tickets to attend a show at the auditorium currently cost $\$4.00$. For each $\$1.00$ increase to the ticket price, $100$ fewer tickets will be sold. This situation can be modeled by the equation $y=-100x^2+\mathrm{1,400}x+\mathrm{7,200}$, where $x$ represents the increase in ticket price, in dollars, and $y$ represents the revenue, in dollars, from ticket sales. If this equation is graphed in the xy-plane, at what value of $x$ is the maximum of the graph?