This paper reports on an exploration of preservice teachers’ understanding of the quadratic function concept in Zimbabwe. These concepts were taught to preservice teachers studying for a diploma in Education wishing to specialize in the teaching of Ordinary level mathematics. Concerns about high Mathematics failure rate in Zimbabwean Secondary Schools have prompted this investigation into finding out if teachers’ understanding of quadratic function concept could be the cause. The study adopted the APOS (action-process-object-schema) to investigate their conceptual understanding of the concepts. Data were generated from students’ responses to a written task and follow up interviews were used to solicit information from the preservice teachers. A designed genetic decomposition for quadratic concepts was used as an analysis tool. The findings of the study also revealed majority of the pre-service teachers seemed to be operating at the action level of understanding, with very few teachers who have reached the object level. It was noted that the preliminary genetic decomposition failed to accommodate all students’ responses which lead to the development of a modified genetic decomposition.