Question

mon core algebra i b - cr
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 the graph crosses the x-axis at $(1,0)$ and $(-4,0)$.

Step2: Determine parabola direction

Expand the function:

$$\begin{align*} f(x)&=(x-1)(x+4)\\ &=x^2 + 3x -4 \end{align*}$$

The coefficient of $x^2$ is $1>0$, so the parabola opens upwards.

Step3: Match to correct graph

Only the bottom-right graph opens upwards and has x-intercepts at $x=1$ and $x=-4$.

Answer:

The bottom-right graph (opening upwards, crossing x-axis at x=1 and x=-4, vertex below the x-axis)