Answer
See below
Work Step by Step
The local maximum is $(-0.4,0.3)$.
The local minimum is about $0.8,-1.4$.
All zeros can be at $x\approx -0.7,x=0,x\approx1.3$
This could be a 3rd degree function.
You can help us out by revising, improving and updating this answer.
Update this answerAfter you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.