  We examine the model of Two-Dimensional Quadratic Gravity as a consequence of
symmetry breaking within the framework of background field (BF) theory. This
theory is essentially an extension of BF theory, introducing an additional
polynomial term that operates on both the gauge and background fields. We
analyze the theory using the Dirac and Faddeev-Jackiw procedures, determining
the form of the gauge transformation, the full structure of the constraints,
the counting of degrees of freedom, and the generalized Faddeev-Jackiw
brackets. Additionally, we demonstrate the coincidence of the Faddeev-Jackiw
and Dirac's brackets. Finally, we provide some remarks and discuss prospects.
