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Advanced Math / Nonlinear functions Difficulty: Medium

What is an x-coordinate of an x-intercept of the graph of $y = 3 (x - 14) (x + 5) (x + 4)$ in the xy-plane?

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Explanation

The correct answer is either $14$ , $negative 5$ , or $negative 4$ . The x-intercepts of a graph in the xy-plane are the points at which the graph intersects the x-axis, or when the value of $y$ is $0$ . Substituting $0$ for $y$ in the given equation yields $0 = 3 (x - 14) (x + 5) (x + 4)$ . Dividing both sides of this equation by $3$ yields $0 = (x - 14) (x + 5) (x + 4)$ . Applying the zero product property to this equation yields three equations: $x - 14 = 0$ , $x + 5 = 0$ , and $x + 4 = 0$ . Adding $14$ to both sides of the equation $x - 14 = 0$ yields $x equals 14$ , subtracting $5$ from both sides of the equation $x + 5 = 0$ yields $x = - 5$ , and subtracting $4$ from both sides of the equation $x + 4 = 0$ yields $x = - 4$ . Therefore, the x-coordinates of the x-intercepts of the graph of the given equation are $14$ , $negative 5$ , and $negative 4$ . Note that 14, -5, and -4 are examples of ways to enter a correct answer.