Abstract: In the 1980s, some research in noncommutative algebra has been driven by attempts to classify Artin-Schelter regular (AS-regular) algebras. Such algebras are often considered to be noncommutative analogues of polynomial rings. Around this time, M. Artin, J. Tate, and M. Van den Bergh introduced the concept of point module, to which one can associate a point in projective space. The authors also introduced a method to compute a scheme that parametrizes the point modules (later called the point scheme by Vancliff and Van Rompay) over a graded algebra generated by elements of degree one. In this presentation, we discuss the family of quadratic algebras A on n+1 generators that have n(n+1)/2 defining relations, where A is an Ore extension of a twist, by an automorphism, of the polynomial ring on n generators. We will end the presentation by discussing specific examples of A where n=3 and n=4 (primarily, the point scheme and the zero locus of the defining relations of A).