1952 AMC 12 Problem 40

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.