SAT Math Multiple Choice Practice Question 246: Answer and Explanation

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Question: 246


The figure above shows the graph of a quadratic function f that has a minimum value when . If , then which of the following could be the value of k?

A. -1
B. 1
C. 2
D. 3
E. 4

Correct Answer: A


A Since f is a quadratic function, its graph is a parabola with a vertical axis of symmetry through its vertex, which in this case is the line . This means that, for any given point on the graph, its reflection over x = 2 is also on the graph. Notice from the given graph that the value of f (5) is about 2.5, as shown above. If we reflect this point, (5, 2.5) over the axis of symmetry, we get the point (–1, 2.5). In other words,, so .

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