Use the x-intercepts to write $f(x)$ as $a(x-r_1)^{m}(x-r_2)^{n}$, where the exponents depend on whether the graph crosses or bounces.

After you have the right factors, plug in the coordinate of the plotted point (the y-intercept is shown) to determine the constant multiplier $a$.

Enter each answer choice as a separate function, for example:

• $y_1=(x+2)^2(x-1)$
• $y_2=2(x+2)^2(x-1)$
• $y_3=-(x+2)^2(x-1)$
• $y_4=(x+2)(x-1)^2$

For each graph, check whether it:

• touches (bounces off) the x-axis at $x=-2$,
• crosses the x-axis at $x=1$,
• passes through the point $(0,-4)$.

The correct choice is the one whose graph matches all of those features at the same time (both intercept behaviors and the y-intercept point).

The graph has zeros at $x=-2$ and $x=1$.

• At $x=-2$, the curve touches the x-axis and turns back down, so $(x+2)$ must have an even power (most simply, power $2$).

• At $x=1$, the curve crosses the x-axis, so $(x-1)$ must have an odd power (most simply, power $1$).

So $f(x)$ must have the form $f(x)=a(x+2)^2(x-1)$ for some constant $a$.

The graph shows the point $(0,-4)$ on the curve.

Substitute $x=0$ into $f(x)=a(x+2)^2(x-1)$:

So $a=1$.

With $a=1$, the function is $f(x)=(x+2)^2(x-1)$, which matches one choice exactly.

Therefore, the correct choice is $(x+2)^2(x-1)$.