What is an x -coordinate of an x -intercept of the graph of y = 3 x - 14 x

Question

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?

Accepted Answer

The correct answer is either 14 , - 5 , or - 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 = 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 , - 5 , and - 4 . Note that 14, -5, and -4 are examples of ways to enter a correct answer.

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