Question

图中给出了 $f(x) = ax^3 + bx^2 + cx + d$ 的部分图像。求 $b$ ？

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

$-4$

$-2$

$0$

$2$

$4$

图像经过 $(-1, 0)$ ， $(1, 0)$ ，和 $(0, 2)$ 。所以 $f(0) = d = 2$ 。

将两式相加：因此 $b = -d = -2$ 。 $\begin{aligned} &f(1) + f(-1) \\ &= (a + b + c + d) \\ &\quad {}+ (-a + b - c + d) \\ &= 2b + 2d = 0, \end{aligned}$

因此，正确答案是 B。

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

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

Thus, the correct answer is B.