New Constructions of Quadratic Bent Functions in Polynomial Form

New quadratic bent functions in polynomial form are constructed in this paper. The constructions give new Boolean bent, generalized Boolean bent and p-ary bent functions. Based on Z₄-valued quadratic forms, a simple method provides several new constructions of generalized Boolean bent functions. From these generalized Boolean bent functions a method is presented to transform them into Boolean bent and semi-bent functions. Moreover, many new p-ary bent functions can also be obtained by applying similar methods.