Question

In order to draw a graph of $f(x)=ax^2+bx+c,$ 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:

$4096$

$4356$

$4489$

$4761$

None of these

Answer: E

Concepts:quadratic pattern recognition perfect square

Difficulty rating: 1410

Small Hint:

A quadratic sampled at equally spaced inputs has constant second differences

Big Hint:

The surrounding values also suggest consecutive perfect squares; check every displayed table value before checking which values appear among the choices

Solution:

The values are intended to be the consecutive squares $\begin{gathered} 62^2,63^2,64^2,65^2,\\ 66^2,67^2,68^2,69^2. \end{gathered}$ These are $3844,3969,4096,4225,$ $4356,4489,4624,4761.$ Thus the incorrect table entry is $4227,$ but it is not one of choices A-D.

Consequently none of the four listed numbers is incorrect, so the correct answer is E.

1952 AMC 12 Problem 40

Answer: E

Difficulty rating: 1410

Small Hint:

Big Hint:

Solution:

Problem 40 in Other Years