In this article we explore the consequences of modifying the common definition of a parabola by considering the locus of all points equidistant from a focus and (not necessarily linear) directrix. The resulting derived curves, which we call "generalized parabolas," are often quite beautiful and possess many interesting properties. We show that the conic sections are generalized parabolas whose directrix is a circle or a line, and their well known reflective properties are actually specific instances of a reflective property held by all generalized parabolas. Finally, we offer the reader suggestions for further investigation.