1. Deriving the Quadratic Formula
Complete the square!

2. The Quadratic Formula
The quadratic formula is give you the solutions to ax2 + bx + c = 0 in terms of a, b, and c.
The formula:
Where did this formula come from? The following slides will show how it’s derived.

3. Derivation
Begin with ax2 + bx + c = 0 . Divide both sides of the equation by a to get x2 + (b/a)x + (c/a) = 0. Subtract c/a from both sides of the equation. x2 + (b/a)x = -c/a

4. Derivation Continued
We have x2 + (b/a)x = -c/a. We want to complete the square on the left side so that we can solve for x. To complete the square, we need to add to both sides of the equation. This gives us

5. Derivation Continued Notice that is in the form
x2+2yx+y2, as we intended. We can factor this as (x+y)2, so we have
Now let’s solve for x.

6. Derivation Continued

7. Derivation Continued

8. Derivation Finale