Answer
$[2-\sqrt 5,2+\sqrt 5]$
Work Step by Step
Step 1. Graph $f(x)=-x^2+4x+1$ as shown in the figure.
Step 2. The solutions to $f(x)=0$ can be found using the quadratic formula as $x=2\pm\sqrt 5$
Step 3. The interval for $f(x)\ge0$ can be identified from the graph as $[2-\sqrt 5,2+\sqrt 5]$
