Question

Solve the inequality by using the graph of the function.

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

$f\left(x\right)=(x+4){(x-2)}^2$

Short answer

The solution of the inequality is $[-4,\infty )$.

Step-by-step solution

Step 1. Given Information 

We are given a function,

$f\left(x\right)=(x+4)(x-2{)}^2$

Step 2. Graphing the function  

The graph of the function is as follows,

Step 3. Solve the inequality  

As seen from the graph, $f\left(x\right)\ge 0$for $[-4,\infty )$.

Hence the solution of the inequality is $[-4,\infty )$.