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## Wednesday, March 27, 2013

The question above is from the January 2013 New York State Regents exam in Integrated Algebra.

It is an example of a well-intentioned, but poorly designed, question.

Simply put, the student who has absolutely no idea, and randomly guesses, has 25% chance of selecting the correct answer.

The student who knows exactly how to graph the quadratic, who can plot its parabolic shape with mastery, and can state the coordinates of its vertex, state the axis of symmetry, identify its intercepts, and so on, but happens to forget the "number names" of the quadrants, has a 25% of selecting the correct answer.

The student who knows everything that the second student knows, but remembers that quadrant I is to the northeast, but forgets whether they are numbered in a clockwise or counterclockwise manner, will select choice (3), the correct answer, since the vertex lies in the southwest quadrant.

The student who knows everything that the second student knows, but believes that quadrant I is to the northwest,and remembers that they are numbered in a clockwise manner, will select choice (4), the an incorrect answer, and have a 0% chance of getting this question answered correctly.

My question is this: What is question 14 actually measuring?