2003 AMC 12B Problem 20

Attempt Problem 20 of the 2003 AMC 12B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 12B solutions, or check the answer key.

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20.

Part of the graph of

f(x) = ax^3 + bx^2 + cx + d

is shown. What is

b?

-4

-2

0

2

4

Read off

f(-1) = 0,

f(1) = 0,

and

f(0) = 2

from the graph

Adding

f(1) + f(-1)

eliminates

a

and

c,

leaving

2b + 2d = 0

The graph passes through

(-1, 0),

(1, 0),

and

(0, 2).

f(0) = d = 2.

Adding

\begin{aligned} &f(1) + f(-1) \\ &= (a + b + c + d) \\ &\quad {}+ (-a + b - c + d) \\ &= 2b + 2d = 0, \end{aligned}

b = -d = -2.

Thus, the correct answer is B.

Problem 20 in other years