SAT Question c7a187a7: Nonlinear Functions answer and explanation with Desmos solution

Choice A is correct. It's given that $y=f\left(x\right)$. The x-intercepts of a graph in the xy-plane are the points where $y=0$. Thus, for an x-intercept of the graph of function $f$, $0=f\left(x\right)$. Substituting $0$ for $f\left(x\right)$ in the equation $f\left(x\right)=x^2-18x-360$ yields $0=x^2-18x-360$. Factoring the right-hand side of this equation yields $0=\left(x+12\right)\left(x-30\right)$. By the zero product property, $x+12=0$ and $x-30=0$. Subtracting $12$ from both sides of the equation $x+12=0$ yields $x=-12$. Adding $30$ to both sides of the equation $x-30=0$ yields $x=30$. Therefore, the x-intercepts of the graph of $y=f\left(x\right)$ are $\left(-12,0\right)$ and $\left(30,0\right)$. Of these two x-intercepts, only $\left(-12,0\right)$ is given as a choice.