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Advanced Math / Nonlinear functions Difficulty: Medium

$f (x) = x^{2} - 18 x - 360$

If the given function $f$ is graphed in the xy-plane, where $y = f (x)$ , what is an x-intercept of the graph?

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Explanation

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 $y equals 0$ . Thus, for an x-intercept of the graph of function $f$ , $0 equals f left parenthesis x right parenthesis$ . Substituting $0$ for $f (x)$ in the equation $f (x) = x^{2} - 18 x - 360$ yields $0 = x^{2} - 18 x - 360$ . 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 $x equals 30$ . Therefore, the x-intercepts of the graph of $y = f (x)$ are $left parenthesis negative 12 comma 0 right parenthesis$ and $left parenthesis 30 comma 0 right parenthesis$ . Of these two x-intercepts, only $left parenthesis negative 12 comma 0 right parenthesis$ 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.