1. 9.5 - The Quadratic Formula

2. Quadratic Equation: x = -b ± √b2 – 4ac

3. Quadratic Equation: x = -b ± √b2 – 4ac
for any quadratic equation in the form
ax2 + bx + c = 0

4. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.

5. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0

6. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0; a = 1

7. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0; a = 1, b = 4,

8. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0; a = 1, b = 4, c = 2

9. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0; a = 1, b = 4, c = 2
x = -b ± √b2 – 4ac 2a

10. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0; a = 1, b = 4, c = 2
x = -b ± √b2 – 4ac 2a
x = -(4) ± √(4)2 – 4(1)(2)
2(1)

11. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0; a = 1, b = 4, c = 2
x = -b ± √b2 – 4ac 2a
x = -(4) ± √(4)2 – 4(1)(2)
2(1)
x = -4 ± √16 – 8 2

12. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0; a = 1, b = 4, c = 2
x = -b ± √b2 – 4ac 2a
x = -(4) ± √(4)2 – 4(1)(2)
2(1)
x = -4 ± √16 – 8 2
x = -4 ± √8

13. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0; a = 1, b = 4, c = 2
x = -b ± √b2 – 4ac 2a
x = -(4) ± √(4)2 – 4(1)(2)
2(1)
x = -4 ± √16 – 8 2
x = -4 ± √8
x = -2 ± ½√8

14. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0; a = 1, b = 4, c = 2
x = -b ± √b2 – 4ac 2a
x = -(4) ± √(4)2 – 4(1)(2)
2(1)
x = -4 ± √16 – 8 2
x = -4 ± √8
x = -2 ± ½√8
x = -2 + ½√8

15. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0; a = 1, b = 4, c = 2
x = -b ± √b2 – 4ac 2a
x = -(4) ± √(4)2 – 4(1)(2)
2(1)
x = -4 ± √16 – 8 2
x = -4 ± √8
x = -2 ± ½√8
x = -2 + ½√8
x ≈ -0.59

16. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0; a = 1, b = 4, c = 2
x = -b ± √b2 – 4ac 2a
x = -(4) ± √(4)2 – 4(1)(2)
2(1)
x = -4 ± √16 – 8 2
x = -4 ± √8
x = -2 ± ½√8
x = -2 + ½√8 x = -2 – ½√8
x ≈ -0.59

17. Ex. 1 a. Solve x2 + 4x + 2 = 0 using the. quadratic formula
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0; a = 1, b = 4, c = 2
x = -b ± √b2 – 4ac 2a
x = -(4) ± √(4)2 – 4(1)(2)
2(1)
x = -4 ± √16 – 8 2
x = -4 ± √8
x = -2 ± ½√8
x = -2 + ½√8 x = -2 – ½√8
x ≈ x ≈ -3.41

18. b. Solve x2 – 5x + 3 = 0 using the. quadratic formula. Round to the
b. Solve x2 – 5x + 3 = 0 using the quadratic formula. Round to the nearest hundredth.

19. b. Solve x2 – 5x + 3 = 0 using the. quadratic formula
b. Solve x2 – 5x + 3 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 – 5x + 3 = 0; a = 1, b = -5, c = 3
x = -b ± √b2 – 4ac 2a
x = -(-5) ± √(-5)2 – 4(1)(3)
2(1)
x = 5 ± √25 – 12 2
x = 5 ± √13
x = ½√13 x = ½√13
x ≈ x ≈ 0.70