  We use the embedding tensor formalism to analyse maximally symmetric
backgrounds of N=2 gauged supergravities which have the full N=2 supersymmetry.
We state the condition for N=2 vacua and discuss some of their general
properties. We show that if the gauged isometries leave the SU(2) R-symmetry
invariant, then the N=2 vacuum must be Minkowski. This implies that there are
no AdS backgrounds with eight unbroken supercharges in the effective N=2
supergravity of six-dimensional SU(3) x SU(3) structure compactifications of
type II string theory and M-theory. Combined with previous results on N=1
vacua, we show that there exist N=2 supergravities with a given set of gauged
Abelian isometries that have both N=2 and N=1 vacua. We also argue that an
analogue of our analysis holds in five and six spacetime dimensions.
