lesson 9.8. warm up evaluate for x = –2, y = 3, and z = –1. 6 1. x 2 2. xyz 3. x 2 – yz4. y...
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![Page 1: Lesson 9.8. Warm Up Evaluate for x = –2, y = 3, and z = –1. 6 1. x 2 2. xyz 3. x 2 – yz4. y – xz 4 5. –x 6. z 2 – xy 71 7 2](https://reader035.vdocument.in/reader035/viewer/2022062300/56649db25503460f94aa180f/html5/thumbnails/1.jpg)
The Quadratic Formula.
a
acbbx
2
42
Lesson 9.8
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Warm Up
Evaluate for x = –2, y = 3, and z =
–1. 6 1. x2 2. xyz
3. x2 – yz 4. y – xz
4
5. –x 6. z2 – xy
7 1
7 2
![Page 3: Lesson 9.8. Warm Up Evaluate for x = –2, y = 3, and z = –1. 6 1. x 2 2. xyz 3. x 2 – yz4. y – xz 4 5. –x 6. z 2 – xy 71 7 2](https://reader035.vdocument.in/reader035/viewer/2022062300/56649db25503460f94aa180f/html5/thumbnails/3.jpg)
California Standards
19.0 Students know the quadratic formula and are familiar with its proof by completing the square. 20.0 Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations.
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![Page 5: Lesson 9.8. Warm Up Evaluate for x = –2, y = 3, and z = –1. 6 1. x 2 2. xyz 3. x 2 – yz4. y – xz 4 5. –x 6. z 2 – xy 71 7 2](https://reader035.vdocument.in/reader035/viewer/2022062300/56649db25503460f94aa180f/html5/thumbnails/5.jpg)
In the previous lesson, you completed the square to solve quadratic
equations. If you complete the square of ax2 + bx + c = 0, you can derive
the Quadratic Formula.
![Page 6: Lesson 9.8. Warm Up Evaluate for x = –2, y = 3, and z = –1. 6 1. x 2 2. xyz 3. x 2 – yz4. y – xz 4 5. –x 6. z 2 – xy 71 7 2](https://reader035.vdocument.in/reader035/viewer/2022062300/56649db25503460f94aa180f/html5/thumbnails/6.jpg)
What Does The Formula Do ?
The Quadratic formula allows you to find the roots of a quadratic equation (if they exist) even if the quadratic equation does not factorise.The formula states that for a quadratic equation of the form :
ax2 + bx + c = 0 The roots of the quadratic equation are given by :
a
acbbx
2
42
![Page 7: Lesson 9.8. Warm Up Evaluate for x = –2, y = 3, and z = –1. 6 1. x 2 2. xyz 3. x 2 – yz4. y – xz 4 5. –x 6. z 2 – xy 71 7 2](https://reader035.vdocument.in/reader035/viewer/2022062300/56649db25503460f94aa180f/html5/thumbnails/7.jpg)
Example 1
Use the quadratic formula to solve the equation :x 2 + 5x + 6= 0Solution:x 2 + 5x + 6= 0a = 1 b = 5 c = 6
a
acbbx
2
42
12
)614(55 2
x
2
)24(255 x
2
15x
2
15
2
15
xorx
x = - 2 or x = - 3
These are the roots of the equation.
![Page 8: Lesson 9.8. Warm Up Evaluate for x = –2, y = 3, and z = –1. 6 1. x 2 2. xyz 3. x 2 – yz4. y – xz 4 5. –x 6. z 2 – xy 71 7 2](https://reader035.vdocument.in/reader035/viewer/2022062300/56649db25503460f94aa180f/html5/thumbnails/8.jpg)
Example 2
Use the quadratic formula to solve the equation :8x 2 + 2x - 3= 0
Solution:
8x 2 + 2x - 3= 0a = 8 b = 2 c = -3
a
acbbx
2
42
82
)384(22 2
x
16
)96(42 x
16
1002x
16
102
16
102
xorx
x = ½ or x = - ¾ These are the roots of the equation.
![Page 9: Lesson 9.8. Warm Up Evaluate for x = –2, y = 3, and z = –1. 6 1. x 2 2. xyz 3. x 2 – yz4. y – xz 4 5. –x 6. z 2 – xy 71 7 2](https://reader035.vdocument.in/reader035/viewer/2022062300/56649db25503460f94aa180f/html5/thumbnails/9.jpg)
Example 3Use the quadratic formula to solve the equation :8x 2 - 22x + 15= 0
Solution:
8x 2 - 22x + 15= 0a = 8 b = -22 c = 15
a
acbbx
2
42
82
)1584()22()22( 2
x
16
)480(484(22 x
16
422x
16
222
16
222
xorx
x = 3/2 or x = 5/4 These are the roots of the equation.
![Page 10: Lesson 9.8. Warm Up Evaluate for x = –2, y = 3, and z = –1. 6 1. x 2 2. xyz 3. x 2 – yz4. y – xz 4 5. –x 6. z 2 – xy 71 7 2](https://reader035.vdocument.in/reader035/viewer/2022062300/56649db25503460f94aa180f/html5/thumbnails/10.jpg)
Because the Quadratic Formula contains a square root, the solutions may be irrational. You can give the exact solution by leaving the square root in your answer, or you can approximate the solutions.
![Page 11: Lesson 9.8. Warm Up Evaluate for x = –2, y = 3, and z = –1. 6 1. x 2 2. xyz 3. x 2 – yz4. y – xz 4 5. –x 6. z 2 – xy 71 7 2](https://reader035.vdocument.in/reader035/viewer/2022062300/56649db25503460f94aa180f/html5/thumbnails/11.jpg)
1. Solve x2 + x = 12 by using the Quadratic Formula.
2. Solve –3x2 + 5x = 1 by using the Quadratic Formula.
3. Solve 8x2 – 13x – 6 = 0. Use at least 2 different methods.
Lesson Quiz
3, –4
= 0.23, ≈ 1.43