Deriving the quadratic formula

Now that students have practice with completing the square, they have all of the tools they need to look at solving quadratic equations more abstractly and derive the quadratic formula. For some students, the algebraic manipulation in this section will seem overwhelming, but for others this section can bring home the connectedness between all they have learned about solving quadratic equations thus far. The main purpose of this section is to derive and build a conceptual understanding of the quadratic formula before using it to solve equations in the next section.