Question

question
find the graph of the polynomial given below.
$f(x)=2(x - 5)(x + 1)(x + 8)$
select the correct answer below:

Explanation:

Step1: Find x-intercepts

Set $f(x)=0$, solve $2(x-5)(x+1)(x+8)=0$.
Roots: $x=5$, $x=-1$, $x=-8$

Step2: Determine end behavior

Degree is 4 (even), leading coefficient $2>0$.
As $x\to\pm\infty$, $f(x)\to+\infty$

Step3: Check y-intercept

Set $x=0$, calculate $f(0)=2(0-5)(0+1)(0+8)=2(-5)(1)(8)=-80$

Answer:

The provided graph is the correct one, as it matches the x-intercepts at $x=-8, -1, 5$, y-intercept at $y=-80$, and the even-degree positive leading coefficient end behavior (rising on both ends).