1. The Quadratic Formula

2. Reminder Form of a quadratic equation: ax2 +bx + c = 0

3. Solve for x: 2x2 + 4x + 1 = 0 No, not factorable
Can we solve by factoring?
No, a > 1
Can we solve by completing the square?

4. The Quadratic Formula:
𝑥= −𝑏± 𝑏 2 −4𝑎𝑐 2𝑎

5. Solve for x: 2x2 + 4x + 1 = 0 a b c 𝑥=
± √ −𝑏
𝑏2 - 4 𝑎 𝑐 2 𝑎

6. Solve for x: 2x2 + 4x + 1 = 0 c a b 𝑥= −4 ± √ −𝑏 42 - 4 𝑏2 - 4 𝑎 𝑐 2 𝑎
(2)
(1) 2
(2) 𝑎

7. Solve for x: 2x2 + 4x + 1 = 0 a b c 𝑥= −4
± √ 𝑥= −4
± √
16 - 8 8 4 4

8. Solve for x: 3x2 - 2x - 4 = 0 a b c 𝑥= ± √ −𝑏 𝑏2 - 4 𝑎 𝑐 2 𝑎 −(−2) (3)
(-2)2 - 4
(3)
(-4) 2
(3) 𝑎

9. Solve for x: 3x2 - 2x - 4 = 0 a b c 𝑥=
± √
± √ 𝑥= 2
4 + 48 2 52 6 6

10. Solve for x: 2x2 - 3x + 6 = 0 a b c ± √ 𝑥= 2 −(−3) (2) (6) (2)
(-3)2 - 4
(2)
(6) 2
(2)

11. Solve for x: 2x2 - 3x + 6 = 0 a b c
± √ 𝑥= 3
9 - 48 4

12. Solve for x: 2x2 - 3x + 6 = 0 a b c ± √ ± √ 𝑥= 4 4 3 3 9 - 48 - 39
No real solutions
± √ 3
9 - 48
± √ 3
- 39 𝑥= 4 4