1. Worksheet Key 9
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4.8 - Quadratic Formula

2. Worksheet Key
(x)2 + 1
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4.8 - Quadratic Formula

3. 11/14/2018 8:58 PM
4.8 - Quadratic Formula

4. Quiz
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4.8 - Quadratic Formula

5. Quadratic Formula Section 4.8 11/14/2018 8:58 PM

6. Discriminant Standard form equation, ax2 + bx + c = 0
Discriminant is from standard form, the expression, b2–4ac indicates how many real number solutions the equation has
To Determine Solutions:
POSITIVE – 2 Real Solutions
ZERO – 1 Solution, Double Root
NEGATIVE – 2 Imaginary Solutions
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4.8 - Quadratic Formula

7. Discriminant: 4, 2 Real Solutions
Example 1
Determine the amount of solutions for this equation and the discriminant of x2 – 4x + 3 = 0
Identify A, B, C first
A: 1, B: –4, C: 3
Plug into equation, b2 – 4ac
(–4)2 – 4(1)(3)
16 – 12 4
Discriminant: 4, 2 Real Solutions
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4.8 - Quadratic Formula

8. Discriminant: 0, 1 Double Root
Example 2
Determine the amount of solutions for this equation and the discriminant of x2 = 8x – 16
Discriminant: 0, 1 Double Root
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4.8 - Quadratic Formula

9. Discriminant: –23, 2 Imaginary Roots
Example 3
Determine the amount of solutions for this equation and the discriminant of –2x2 – 5x – 6 = 0
Discriminant: –23, 2 Imaginary Roots
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4.8 - Quadratic Formula

10. Discriminant: –223, 2 Imaginary Roots
Your Turn
Determine the amount of solutions for this equation and the discriminant of 2x2 + x + 28 = 0
Discriminant: –223, 2 Imaginary Roots
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4.8 - Quadratic Formula

11. Quadratic Formula Quadratic Formula from Completing the Square
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4.8 - Quadratic Formula

12. Quadratic Formula Quadratic Formula from Completing the Square
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4.8 - Quadratic Formula

13. Quadratic Formula Quadratic Formula from Completing the Square
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4.8 - Quadratic Formula

14. Quadratic Formula Quadratic Formula is another way of finding x Steps:
Make sure the equation equals to zero
Identify A, B, C
Plug into equation
Check your work
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4.8 - Quadratic Formula

15. Quadratic Formula
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4.8 - Quadratic Formula

16. Quadratic Formula
X equals negative B, plus or minus square root, b squared minus 4 A C, all over 2 A
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4.8 - Quadratic Formula

17. Example 4
Solve x2 – 4x + 3 = 0 using Quadratic Formula A: 1, B: –4, C: 3
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4.8 - Quadratic Formula

18. Example 4
Solve x2 – 4x + 3 = 0 using Quadratic Formula A: 1, B: –4, C: 3
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4.8 - Quadratic Formula

19. Example 5 Solve 2x2 – 5x = –3 using Quadratic Formula
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4.8 - Quadratic Formula

20. Example 6
Solve x2 + 12x + 9 = 0 using Quadratic Formula A: 1, B: 12, C: 9
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4.8 - Quadratic Formula

21. Example 6
Solve x2 + 12x + 9 = 0 using Quadratic Formula A: 1, B: 12, C: 9
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4.8 - Quadratic Formula

22. Example 7 Solve 9x2 – 11 = 6x using Quadratic Formula
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4.8 - Quadratic Formula

23. Your Turn Solve 2x2 – 10 = 4x using Quadratic Formula
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4.8 - Quadratic Formula

24. Assignment
Worksheet
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4.8 - Quadratic Formula