In the above table, for suitably chosen constants a, b and c, which one of the following best describes the relation between y and x?
Explanation:
In the above table, it can be seen that the values are taken at equal intervals. Also, the second differences i.e. values of ∆2y are constant and hence, the function is actually a polynomial of degree 2.
Thus, y = a + bx + cx2 best describes the relation between y and x.
Hence, option (b).
Alternatively,
The relation between x and is not a line since y2-y1x2-x1 is not a constant.
Also, ea+bx will not be a whole number. Hence, by substituting values from the table, it can be checked that the relation is given by y = a + bx + cx2.
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