Question

Solve the inequality by using the graph of the function.

Solve $f\left(x\right)\le 0$, where

$f\left(x\right)=x(x+2{)}^2$

Short answer

The solution of the inequality is $(-\infty ,0)$.

Step-by-step solution

Step 1. Given Information

We are given a function,

$f\left(x\right)=x(x+2{)}^2$

Step 2. Graphing the function 

The graph of the function $f\left(x\right)=x(x+2{)}^2$is as follows,

Step 3. Solve the inequality 

As seen from the graph, $f\left(x\right)\le 0$for $(-\infty ,0)$.

Hence the solution is$(-\infty ,0)$.