A quadratic parallel manipulator refers to a parallel manipulator with a quadratic characteristic polynomial. This paper revisits the forward displacement analysis (FDA) of a quadratic spherical parallel manipulator: the Agile Eye. An alternative formulation of the kinematic equations of the Agile Eye is proposed. The singularity analysis of the Agile Eye is then dealt with. After an alternative solution to the FDA has been presented, a formula is revealed that produces a unique current solution to the FDA for a given set of inputs. A regular cube in the input-space, which is singularity free, is also proposed for the Agile Eye. This work will facilitate the control of the Agile Eye.