Question 1114588: Which data set represents perfect quadratic data?
A. A table showing data of x and y as (3,-8), (5,2), (7,8), (9,14) and (11,20) respectively.
B. A table showing data of x and y as (-1,16), (0,8), (1,4), (2,2) and (3,1) respectively.
C. A table showing data of x and y as (-4,7), (-1,1), (2,3), (5,9) and (8,15) respectively.
D. A table showing data of x and y as (-5,14), (-3,2), (-1,-2), (1,2) and (3,14) respectively.
Answer by greenestamps(13203)   (Show Source):
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In all four answer choices, the x values are equally spaced; this makes it relatively easy to find the answer to the question.
One way to find the answer is knowing that, in a quadratic function, the graph has an axis of symmetry; the y values are symmetrical. In choice D, the y values are 14, 2, -2, 2, and 14. So
Answer: data set D
A more advanced way of recognizing quadratic data is that, as long as the x values are equally spaced, the second differences in the y values are constant.
For answer choice D, the first differences in the sequence of y values are -12, -4, 4, and 12; the second differences are 8, 8, and 8. That constant second difference tells us the data is quadratic.
None of the other data sets has a constant second difference in the y values, so answer choice D is the only quadratic set of data.
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