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Advanced Math Difficulty: Medium

$f (x) = (x + 6) (x - 4)$

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

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Explanation

The correct answer is either $negative 6$ or $4$ . 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 $y = f (x)$ , $0 equals f left parenthesis x right parenthesis$ . Substituting $0$ for $f (x)$ in the equation $f (x) = (x + 6) (x - 4)$ yields $0 = (x + 6) (x - 4)$ . By the zero product property, $x + 6 = 0$ and $x - 4 = 0$ . Subtracting $6$ from both sides of the equation $x + 6 = 0$ yields $x = - 6$ . Adding $4$ to both sides of the equation $x - 4 = 0$ yields $x equals 4$ . Therefore, the x-coordinates of the x-intercepts of the graph of $y = f (x)$ are $negative 6$ and $4$ . Note that -6 and 4 are examples of ways to enter a correct answer.