1. Derivation of the Quadratic Formula
The following shows how the method of Completing the Square can be used to derive the Quadratic Formula.
Start with the general quadratic equation.
Move the constant to the other side.
Divide by a, the leading coefficient.

2. Complete the square.
Add the value to both sides of the equation.

3. Factor the left side and simplify the right side.

4. Complete the problem using the square root method of solving a quadratic equation.

6. Quadratic Formula
The expression under the radical is called the Discriminant.

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