I tried two different models for a regression (both with one predictor).

The first one was a linear regression model of the type Y= a + bX and the coefficients seem to be statistically significant (at the 95% level) and the coefficient of determination is relatively high : R^2 = 0.85

The second model I used was a model of polynomial regression of the second degree (quadratic regression). I found that the coefficients were NOT statistically significant. However, i found R^2 = 0.89

How should I interpret this?

Btw: I did use the same data set for in both regressions, obviously.

Thank you