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Worksheet Key

Dive into the Quadratic Formula with examples and solutions to enhance your understanding. Learn how to determine the number of solutions using discriminants. Practice equations and sharpen your skills!

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Worksheet Key

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  1. Worksheet Key 9 4.8 - Quadratic Formula

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

  3. 4.8 - Quadratic Formula

  4. Quiz 4.8 - Quadratic Formula

  5. Quadratic Formula Section 4.8 4.8 - Quadratic Formula

  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 4.8 - Quadratic Formula

  7. Example 1 Discriminant: 4, 2 Real Solutions • 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 4.8 - Quadratic Formula

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  24. Assignment Worksheet 4.8 - Quadratic Formula

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