What is the minimum value of the function f defined by ?

Question

Accepted Answer

Choice A is correct. The given quadratic function f is in vertex form, , where is the vertex of the graph of in the xy -plane. Therefore, the vertex of the graph of is . In addition, the y -coordinate of the vertex represents either the minimum or maximum value of a quadratic function, depending on whether the graph of the function opens upward or downward. Since the leading coefficient of f (the coefficient of the term ) is 1, which is positive, the graph of opens upward. It follows that at , the minimum value of the function f is . Choice B is incorrect and may result from making a sign error and from using the x -coordinate of the vertex. Choice C is incorrect and may result from using the x -coordinate of the vertex. Choice D is incorrect and may result from making a sign error.

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