In　this　paper,　we　establish　representation　theorems　for　generators　of　backward　stochastic　differential　equations　(BSDEs　in　short),　whose　generators　are　monotonic　and　convex　growth　in　y　and　quadratic　growth　in　z.　We　also　obtain　a　converse　comparison　theorem　for　such　BSDEs.　(C)　2014　Elsevier　B.V.　All　rights　reserved.