Quadratic Formula Review Geometry 830 1. State the quadratic formula. 2. Which part of this formula represents the discriminant? 3. What does it indicate? 4. On a graph, what would the answer to #3 mean? Identify a, b, and c for the following quadratics. 5. 3x2 + 5x = 2 6. y2 = 7y – 4 8. 6 – 3x2 = 0 9. 2 2 x + 4x + 5 = 0 3 7. 2w2 = 5 10. 3f2 + 4 = 2f Find the value of the discriminant and determine the number of roots for the quadratic. Indicate whether the root is rational, real, or imaginary. 11. x2 + 4x – 4 = 0 12. 2n2 – 5n – 1 = 0 13. 3x2 – 6x + 30 = 0 14. x2 – 4x + 5 = 0 15. y2 = 4y – 1 15. 4x2 + 12x = -9 16, 16x2 + 1 = 8x 17. 2n2 = 5n – 3 18. 5u2 + 6u + 2 =0 19. 6x2 – 4x = -1 20. 15 – 3y2 = 0 21. 6x + 2 = -5x2 Solve using the quadratic formula. Leave irrational roots in simplest radical form. 22. x2 + 5 3 x =0 2 2 24. x(2x -1) – 3(x + 4) = 0 23. 4x (x – 2) = 5(x – 1) 25. x 2 3 x 6 26. x 2 2 x 5 3 27. 2(x + 3)2 = 5(x + 2)2 28. (y + 1)2 – 2(y – 2)2 = 8 29. a2 + 6a + 7 = 0 30. 5a2 + 7a = 6 31. 2y2 – 8y + 3 = 0 32. 6x2 – 4 = 5x 33. x 2 2 4 x 0 3 3 Solve the following quadratics using the quadratic formula and give the answers to the nearest hundredth. 34. 8x2 – 2x = -1 35. 2x2 + 8x = -5 36. y2 + 6y + 4 = 0 37. x2 = -3x + 4 Quadratic Formula Review Answers 1. b b 2 4ac x 2a 2. b 2 4ac 25. x 6 3 2 2 26. x 2 54 2 2 27. x 4 10 3 3. The number of real solutions 4. The number of places the function touches the x-axis 5. a = 3, b = 5, c = -2 28. x 5 10 6. a = 1, b = -7, c = 4 29. x 3 2 7. a = 2, b = 0, c = -5 3 30. x , 2 5 8. a = -3, b = 0, c = 6 9. a = 2, b = 12, c = 15 10. a = 3, b = -2, c = 4 11. 2 real roots 31. x 2 32. x 4 1 , 3 2 33. x 1 13 3 12. 2 real roots 13. 2 imaginary roots 14. 2 imaginary roots 10 2 15. 2 real roots 34. No Real Roots 15. 1 rational root 35. x = -0.78, -3.22 16. 1 rational root 36. x = -0.76, -5.24 17. 2 rational roots 37. x = 1, -4 18. 2 imaginary roots 19. 2 imaginary roots 20. 2 real roots 21. 2 imaginary roots 22. x = ½, -3 23. x 13 89 8 24. x 1 7