Question

question
find the graph of the polynomial given below.
$f(x)=-2(x-3)(x+1)(x+8)$
select the correct answer below:

Explanation:

Step1: Find x-intercepts

Set $f(x)=0$, solve $-2(x-3)(x+1)(x+8)=0$.
Roots: $x=3$, $x=-1$, $x=-8$

Step2: Find y-intercept

Set $x=0$, calculate $f(0)$.
$f(0)=-2(0-3)(0+1)(0+8)=-2(-3)(1)(8)=48$

Step3: Analyze end behavior

Leading term: $-2x^3$. As $x\to+\infty$, $f(x)\to-\infty$; as $x\to-\infty$, $f(x)\to+\infty$.

Step4: Verify given graph

Check intercepts: x-intercepts at -8, -1, 3; y-intercept at 48. End behavior matches: left rises, right falls.

Answer:

The provided graph is the correct graph for $f(x)=-2(x-3)(x+1)(x+8)$ (select the option corresponding to this graph).