Witt kernels of function field extensions in characteristic 2

In characteristic 2 we give a complete characterization of anisotropic symmetric bilinear forms that become metabolic over the function field of a quadratic form. We also study the hyperbolicity of nonsingular quadratic forms over such a field by generalizing some results by Fitzgerald (Pacific J. Math. 109 (1983) 89). As an application, we introduce and study the notion of Pfister neighbors for bilinear forms, and classify anisotropic bilinear forms of height 1, i.e. those that become metabolic over their own function fields. Other consequences are also included.