Curvilinearity test in logistic regression

Hello there,
as a statistics beginner, I have replicated a logistic regression Model for violent conflict spillover and added new variables that I found interesting. One of them (Voice and Accountability, VAA) is related to the regime type of a country, which is usually suspected to have a curvilinear relation with conflict spillover.
Having never actually learned this, I (quite crudely?) tried to test for curvilinearity by including a squared and cubed term for VAA.
I am yet unable to interpret the results: Without including the squared and/or cubed term, VAA is highly significant. Including only the squared or both squared and cubed terms, all 3 variables show no significance at all.
What can be deducted from this for
a) the curvilinearity and
b) the "actual" signficance of VAA?
If anything can be deducted from this observation in general. I am sorry if I missed to provide further relevant information, please ask for it, then!
Thank you very much in advance!
Helpless student


Less is more. Stay pure. Stay poor.
Can you describe VAA in more detail how it is formatted, distributed, etc.

Can you plot the predicted probabilities of the outcome given VAA and see the shape of the graph.