9.5 - The Quadratic Formula

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

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

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.

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

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

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,

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

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

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)

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

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

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

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

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

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

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 x ≈ -3.41

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.

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 = 2.5 + ½√13 x = 2.5 + ½√13 x ≈ 4.30 x ≈ 0.70