1. Quadratic Formula

2. What is the quadratic formula?
𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎

3. Does that look complicated?
𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎

4. It’s not!!!!!!!!!!!!

5. Example:
𝒙 𝟐 +𝟔𝒙−𝟕=𝟎 We can factor this and get: 𝑥+7 𝑥−1 =0 We can then solve and get: 𝑥=−7,𝑥=1

6. Solving using quadratic formula:
𝒙 𝟐 +𝟔𝒙−𝟕=𝟎
Use this:
𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎

7. Solving using quadratic formula:
𝒙 𝟐 +𝟔𝒙−𝟕=𝟎
Get this:
𝑥= −6± −4∗1∗−7 2∗1

8. 𝑥= −6± −4(1)(−7) 2(1)
𝑥=−7 𝑎𝑛𝑑 𝑥=1

9. Remember:
Don’t forget to find the PLUS and MINUS versions of the answer. You will often have 2 solutions!

10. 𝟐 𝒙 𝟐 +𝟕𝒙+𝟔=𝟎 Use quadratic formula: 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎
Another example:
𝟐 𝒙 𝟐 +𝟕𝒙+𝟔=𝟎 Use quadratic formula: 𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎

11. Identify A, B, C:
𝟐 𝒙 𝟐 +𝟕𝒙+𝟔=𝟎 A= B= C=

12. 𝑥= −7± −4(2)(6) 2(2)

13. Odd looking answers
𝒙 𝟐 −𝟓𝒙+𝟐

14. Odd looking answers
𝒙 𝟐 −𝟓𝒙+𝟐
𝒙= −(−𝟓)± (−𝟓) 𝟐 −𝟒∗𝟏∗𝟐 𝟐∗𝟏

15. 𝑥= 𝑥= 5− 17 2

17. Odd looking answer (2):
𝟐 𝒙 𝟐 +𝟑𝒙+𝟓

18. 𝟐 𝒙 𝟐 +𝟑𝒙+𝟓 𝒙= −𝟑± 𝟑 𝟐 −𝟒∗𝟐∗𝟓 𝟐∗𝟐

19. No solution!!!!!

20. 𝟐 𝒙 𝟐 +𝟑𝒙+𝟓