Nonlinear functions SAT question

Choice A is correct. It's given that $y=f(x)$. 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 $f$, $0=f(x)$. Substituting $0$ for $f(x)$ in the equation $f(x)=x^2-18x-360$ yields $0=x^2-18x-360$. Factoring the right-hand side of this equation yields $0=(x+12)(x-30)$. 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 $y=f(x)$ are $(-12,0)$ and $(30,0)$. Of these two x-intercepts, only $(-12,0)$ is given as a choice.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.