Nonlinear　Schrodinger　equation　with　simple　quadratic　potential　modulated　by　a　spatially-varying　diffraction　coefficient　is　investigated　theoretically.　Second-order　rogue　wave　breather　solutions　of　the　model　are　constructed　by　using　the　similarity　transformation.　A　modal　quantum　number　is　introduced,　useful　for　classifying　and　controlling　the　solutions.　From　the　solutions　obtained,　the　behavior　of　second　order　Kuznetsov-Ma　breathers　(KMBs),　Akhmediev　breathers　(ABs),　and　Peregrine　solitons　is　analyzed　in　particular,　by　selecting　different　modulation　frequencies　and　quantum　modal　parameter.　We　show　how　to　generate　interesting　second　order　breathers　and　related　hybrid　rogue　waves.　The　emergence　of　true　rogue　waves　-　single　giant　waves　that　are　generated　in　the　interaction　of　KMBs,　ABs,　and　Peregrine　solitons　-is　explicitly　displayed　in　our　analytical　solutions.　(C)2015　Optical　Society　of　America