Question

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 $x=-4$, so intercepts at $(1,0)$ and $(-4,0)$.

Step2: Determine parabola direction

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

Step3: Find y-intercept

Set $x=0$: $f(0)=(0-1)(0+4)=-4$, so y-intercept at $(0,-4)$.

Step4: Match to graph

Only the top-right graph has upward opening, x-intercepts at $1$ and $-4$, and y-intercept at $-4$.

Answer:

The top-right graph (the third option with upward-opening parabola passing through $(-4,0)$, $(1,0)$, and $(0,-4)$)