We consider a mathematical model that consists of a nematic liquid crystal layer sandwiched between two parallel bounding plates, across which an external field is applied. We investigate how the number and type of solutions for the director orientation within the layer change as the field strength, anchoring conditions, and material properties of the nematic liquid crystal layer vary. In particular, we focus on how the inclusion of flexoelectric effects alters the Freedericksz and saturation thresholds.