Question

Se muestra parte de la gráfica de $f(x) = ax^3 + bx^2 + cx + d$ . ¿Cuánto vale $b$ ?

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

$-4$

$-2$

$0$

$2$

$4$

La gráfica pasa por $(-1, 0),$ $(1, 0),$ y $(0, 2).$ Así que $f(0) = d = 2.$

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

Por lo tanto, la respuesta correcta es 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.