Question

4. Is the following relation linear, quadratic or cubic? If it is linear, find the equation. Explain your reasoning and include all your work in your final answer; P = {(x, y), (1 ,3), (2,9), (3,17), (4,27) ,(5,39) ,(6,53)}

Answer 1

The following relation P = {(x, y), (1 ,3), (2,9), (3,17), (4,27) ,(5,39) ,(6,53)} is a quadratic relation by virtue of its second differences.

Quadratic relation

The kind of function which is defined by the pair of coordinates as given in the task content can be determined by assessing the first, second or third differences in y-values at a constant increment of x.

Hence, for the pair of coordinates given, we have;

P = {(x, y), (1 ,3), (2,9), (3,17), (4,27) ,(5,39) ,(6,53)}

First differences are; +6, +8, +10, +12, +14.

Hence, since the differences are not constant, we must check for the second differences;

Second differences; +2, + 2, +2, +2.

On this note, since the second differences are constant, it follows that the relation in discuss represents a quadratic function.

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