Ans: A
Note that the two $x$-intercepts of the graph $y=f(x)$ are $-1$ and $4$. Then let $f(x)=a(x-(-1))(x-4)$, where $a$ is a constant. Note also that the graph passes through the point $(0,-2)$, then we have
Note that the two $x$-intercepts of the graph $y=f(x)$ are $-1$ and $4$. Then let $f(x)=a(x-(-1))(x-4)$, where $a$ is a constant. Note also that the graph passes through the point $(0,-2)$, then we have
$\begin{array}{rcl}
f(0) & = & -2 \\
a(0+1)(x-4) & = & -2 \\
-4a & = & -2 \\
a & = & \dfrac{1}{2}
\end{array}$
Therefore, $f(x)= \dfrac{1}{2}(x+1)(x-4)$.
