We study quadratic Boolean functions f from F2n to F2, which are well-known to have plateaued Fourier spectrum Fs;f , i.e., their Fourier coefficients are in the set {0,+_2(n+s)/2 } for some integer 0 ≤ s ≤ n-1. For various types of integers n, we determine possible values of s, construct f with Fs;f for a prescribed s, and present enumeration results in case n is a power of 2. Our work generalizes some of the earlier results of Khoo et. al. ([5]) on near-bent functions and provides a simple proof of a result of Fitzgerald ([2]) on degenerate quadratic forms.