How to Derive the Quadratic Formula.pptx

Deriving the Quadratic Formula | Standard Form Quadratic Equation | The Qauadratic Formular | Completing the Square

1. Deriving the Quadratic Formula By Mahen Mahindaratne MBA, LLB

2. We start with the standard form quadratic equation, which is , and we divide the entire equation by a: Then we move the constant to the other side: =  

3. Completing the Square To complete the square, we need to add and subtract the square of half the coefficient of 𝑥. The coefficient of 𝑥 is , and half of this is . And the square of this is  

4. This can be simplified as: , can further be simplified as  

5. Next, remove the square on the left by including the , of the right side of the equation: = This can be simplified as: = Next, we move everything to the right, to derive the quadratic formular:  

6. When the Discriminant is positive, we get two real solutions. When it is zero we get just ONE real solution (both answers are the same). When it is negative we get a pair of Complex solutions using Imaginary Numbers. If you were to take the long form solution, and factor the quadratic, to derive what the multiples are, then the factor multiples will be the roots of the equation, where is zero.  

7. Completing the Square https://www.mathsisfun.com/algebra/completing-square.html

8. Thank you!