SAT Question ebed7dc6: Nonlinear Functions answer and explanation with Desmos solution

Choice B is correct. It's given that the situation can be modeled by the equation $y=-100x^2+1,400x+7,200$, where $x$ represents the increase in ticket price, in dollars, and $y$ represents the revenue, in dollars, from ticket sales. Since the coefficient of the $x^2$ term is negative, the graph of this equation in the xy-plane opens downward and reaches its maximum value at its vertex. If a quadratic equation in the form $y=a{x}^2+bx+c$, where $a$, $b$, and $c$ are constants, is graphed in the xy-plane, the x-coordinate of the vertex is equal to $-\frac{b}{2a}$. For the equation $y=-100x^2+1,400x+7,200$, $a=-100$, $b=1,400$, and $c=7,200$. It follows that the x-coordinate of the vertex is $-\frac{1,400}{2(-100)}$, or $7$. Therefore, if the given equation is graphed in the xy-plane, the maximum of the graph occurs at an x-value of $7$.