Question

The formula expressing the relationship between $x$ and $y$ in the table is:

$x$	$2$	$3$	$4$	$5$	$6$
$y$	$0$	$2$	$6$	$12$	$20$

$y=2x-4$

$y=x^2-3x+2$

$y=x^3-3x^2+2x$

$y=x^2-4x$

$y=x^2-4$

Answer: B

Concepts:data and graph interpretation quadratic pattern recognition

Difficulty rating: 1390

Small Hint:

The first differences $2,4,6,8$ suggest a quadratic rule

Big Hint:

The values are $(x-1)(x-2)$

Solution:

The $y$ -values factor naturally as $\begin{gathered} 0=1\cdot0,\quad 2=2\cdot1,\quad 6=3\cdot2,\\ 12=4\cdot3,\quad 20=5\cdot4. \end{gathered}$ Thus $y=(x-1)(x-2)$ and hence $y=x^2-3x+2.$

Thus, the correct answer is B.

1951 AMC 12 Problem 41

Answer: B

Difficulty rating: 1390

Small Hint:

Big Hint:

Solution:

Problem 41 in Other Years