9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.
19
9.5 - The Quadratic Formula
-
Upload
rolf-benson -
Category
Documents
-
view
224 -
download
0
Transcript of 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.
9.5 - The Quadratic Formula
• Quadratic Equation: x = -b ± √b2 – 4ac
2a
• Quadratic Equation: x = -b ± √b2 – 4ac
2a
for any quadratic equation in the form
ax2 + bx + c = 0
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. Round to the nearest hundredth.
x2 + 4x + 2 = 0
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. 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. 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. 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. 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. 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. 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
2
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
2 x = -2 ± ½√8
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
2 x = -2 ± ½√8
x = -2 + ½√8
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
2 x = -2 ± ½√8
x = -2 + ½√8 x ≈ -0.59
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
2 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. 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
2 x = -2 ± ½√8
x = -2 + ½√8 x = -2 – ½√8x ≈ -0.59 x ≈ -3.41
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. 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
2x = 2.5 + ½√13 x = 2.5 + ½√13x ≈ 4.30 x ≈ 0.70
