The Quadratic Formula

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

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?

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

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

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

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

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

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

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

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

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