9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.
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Transcript of 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.
![Page 1: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/1.jpg)
9.5 - The Quadratic Formula
![Page 2: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/2.jpg)
• Quadratic Equation: x = -b ± √b2 – 4ac
2a
![Page 3: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/3.jpg)
• Quadratic Equation: x = -b ± √b2 – 4ac
2a
for any quadratic equation in the form
ax2 + bx + c = 0
![Page 4: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/4.jpg)
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
![Page 5: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/5.jpg)
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0
![Page 6: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/6.jpg)
Ex. 1 a. Solve x2 + 4x + 2 = 0 using the quadratic formula. Round to the nearest hundredth.
x2 + 4x + 2 = 0; a = 1
![Page 7: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/7.jpg)
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,
![Page 8: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/8.jpg)
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
![Page 9: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/9.jpg)
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
![Page 10: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/10.jpg)
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)
![Page 11: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/11.jpg)
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
![Page 12: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/12.jpg)
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
![Page 13: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/13.jpg)
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
![Page 14: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/14.jpg)
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
![Page 15: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/15.jpg)
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
![Page 16: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/16.jpg)
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
![Page 17: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/17.jpg)
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
![Page 18: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/18.jpg)
b. Solve x2 – 5x + 3 = 0 using the quadratic formula. Round to the
nearest hundredth.
![Page 19: 9.5 - The Quadratic Formula. Quadratic Equation: x = -b ± √b 2 – 4ac 2a.](https://reader036.fdocuments.net/reader036/viewer/2022082407/5697bff81a28abf838cbf1fa/html5/thumbnails/19.jpg)
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