f x = x - 44 x - 46 The function f is defined by the given equation. For what

Question

f x = x - 44 x - 46 The function f is defined by the given equation. For what value of x does f x reach its minimum?

Accepted Answer

Choice B is correct. It's given that f x = x - 44 x - 46 , which can be rewritten as f x = x 2 - 90 x + 2,024 . Since the coefficient of the x 2 -term is positive, the graph of y = f x in the xy -plane opens upward and reaches its minimum value at its vertex. For an equation in the form f x = a x 2 + b x + c , where a , b , and c are constants, the x -coordinate of the vertex is - b 2 a . For the equation f x = x 2 - 90 x + 2,024 , a = 1 , b = - 90 , and c = 2,024 . It follows that the x -coordinate of the vertex is - - 90 2 1 , or 45 . Therefore, f x reaches its minimum when the value of x is 45 . Choice A is incorrect. This is one of the x -coordinates of the x -intercepts of the graph of y = f x in the xy -plane. Choice C is incorrect. This is one of the x -coordinates of the x -intercepts of the graph of y = f x in the xy -plane. Choice D is incorrect. This is the y -coordinate of the vertex of the graph of y = f x in the xy -plane.

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