A substantial body of research has documented that the types of knowledge that mathematics teachers draw upon during their practice often differs from the knowledge of individuals working in other fields. Drawing on the Mathematical Knowledge for Teaching (MKT) Framework and the School Mathematics Teaching Pedagogical Content Knowledge (SMTPCK) Framework, we investigated the knowledge that mathematics preservice secondary teachers (M-PSTs) used when solving quadratic equations and talking about teaching this topic during task-based interviews. Most of the M-PSTs were able to draw on their Common Content Knowledge (in MKT) and Content Knowledge in a Pedagogical Context (in SMTPCK) for procedures such as using the quadratic formula and completing the square. the M-PSTs, however, more often struggled and expressed uncertainty when asked to draw on their Specialised Content Knowledge (in MKT) and Clearly Pedagogical Content Knowledge (in SMTPCK) to, for example, provide multiple representations to support student learning. Our findings support persistent calls from professional organisations for a series of courses in secondary mathematics teacher education programs that provide opportunities for M-PSTs to engage with and investigate secondary mathematics content from an advanced perspective. Such experiences have the potential to enhance development of several domains of M-PSTs' MKT and SMTPCK. Similarities, differences, affordances, and limitations of MKT and SMTPCK frameworks are discussed.