which is the graph of $f(x) = (x - 1)(x + 4)$?

Explanation:

Step1: Find x-intercepts

Set $f(x)=0$, solve $(x-1)(x+4)=0$. Solutions: $x=1$ and $x=-4$.

Step2: Determine parabola direction

Expand $f(x)=x^2+3x-4$. The coefficient of $x^2$ is $1>0$, so parabola opens upward.

Step3: Calculate vertex x-coordinate

Use midpoint of intercepts: $x=\frac{1+(-4)}{2}=-\frac{3}{2}=-1.5$.

Step4: Calculate vertex y-value

Substitute $x=-1.5$ into $f(x)$: $f(-1.5)=(-1.5-1)(-1.5+4)=(-2.5)(2.5)=-6.25$.

Answer:

The graph is the first one (top-left), which opens upward, has x-intercepts at $x=-4$ and $x=1$, and a vertex at $(-1.5, -6.25)$.