Problem: In order to draw a graph of f(x)=ax2+bx+c, a table of values was constructed. These values of the function for a set of equally spaced increasing values of x were 3844,3969,4096,4227,4356,4489,4624, and 4761. The one which is incorrect is:
Answer Choices:
A. 4096
B. 4356
C. 4489
D. 4761
E. none of these
Solution:
We are told that the values of f(x) listed correspond to
f(x),f(x+h),f(x+2h),⋯,f(x+7h).
Observe that the difference between successive values is given by
f(x+h)−f(x)=a(x+h)2+b(x+h)+c−(ax2+bx+c)=2ahx+ah2+bh.
Since this difference is a linear function of x, it must change by the same amount whenever x is increased by h. But the successive differences of the listed values
are38441253969127409613142271294356133448913546241374761
so that, if only one value is incorrect, 4227 is that value.