In　this　paper,　we　establish　a　general　representation　theorem　for　generator　of　backward　stochastic　differential　equation　(BSDE),　whose　generator　has　a　quadratic　growth　in　z.　As　some　applications,　we　obtain　a　general　converse　comparison　theorem　of　such　quadratic　BSDEs　and　uniqueness　theorem,　translation　invariance　for　quadratic　g-expectation.