f x = x 2 - 18 x - 360 If the given function f is graphed in the xy

Question

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?

Accepted Answer

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 - 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 = 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.

Question f-x-x-