Quadratic utility: monotonicity and risk aversion

Quadratic utility is given by $$u(w) = w - b w^2$$ which has derivative $$u'(w) = 1- 2b w$$ such that for high levels of $w, u'(w)<0$. That is, the utility is not everywhere increasing. This may be weird because even people with high wealth should prefer more to less. The second derivative is $$u'(w) = -2b$$ such that absolute risk aversion is $$frac{- u''(w)}{u'(w)} = frac{ 2b}{1- 2b w},$$ which is increasing in wealth. This contradicts evidence that wealthier people take more financial risks instead of less.