IM Alg1.7.19 Lesson: Deriving the Quadratic Formula
Here are some perfect squares in factored and standard forms, and an expression showing how the two forms are related. Study the first few examples, and then complete the missing numbers in the rest of the table.
Look at the expression in the last row of the table. If is equivalent to , how are , and related to and ?
One way to solve the quadratic equation is by completing the square. A partially solved equation is shown here. Study the steps. Then, knowing that is a placeholder for , continue to solve for but without evaluating any part of the expression. Be prepared to explain each step.
Explain how the solution is related to the quadratic formula.
Here is one way to make sense of how the quadratic formula came about. Study the derivation until you can explain what happened in each step. Record your explanation next to each step.
Here is another way to derive the quadratic formula by completing the square.
The beginning steps of this approach are shown here. Briefly explain what happens in each step.
Continue the solving process until you have the equation .