2003 AMC 12B Problem 20 — Solution | LIVE by Po-Shen Loh

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2003 AMC 12B Problem 20

Below is the professionally curated solution for Problem 20 of the 2003 AMC 12B, 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.

All of the real AMC 8, AMC 10, AMC 12, and AIME problems in our complete solution collection are used with official legal permission of the Mathematical Association of America (MAA).

Concepts:polynomial substitution

Difficulty rating: 1580

20.

Part of the graph of $f(x) = ax^3 + bx^2 + cx + d$ is shown. What is $b?$

$-4$

$-2$

$0$

$2$

$4$

Solution:

The graph passes through $(-1, 0),$ $(1, 0),$ and $(0, 2).$ So $f(0) = d = 2.$

Adding $f(1) + f(-1) = (a + b + c + d) + (-a + b - c + d) = 2b + 2d = 0,$ so $b = -d = -2.$

Thus, the correct answer is B.

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