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11.3 Solving Quadratic Equations by the Quadratic Formula

11.3 Solving Quadratic Equations by the Quadratic Formula. Objective 1 . Derive the quadratic formula. Slide 11.3- 2. Derive the quadratic formula. Solve ax 2 + bx + c = 0 by completing the square (assuming a > 0). Slide 11.3- 3. Derive the quadratic formula. Slide 11.3- 4.

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11.3 Solving Quadratic Equations by the Quadratic Formula

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  1. 11.3 Solving Quadratic Equations by the Quadratic Formula

  2. Objective 1 Derive the quadratic formula. Slide 11.3- 2

  3. Derive the quadratic formula. Solve ax2 + bx + c = 0 by completing the square (assuming a > 0). Slide 11.3- 3

  4. Derive the quadratic formula. Slide 11.3- 4

  5. Derive the quadratic formula. Slide 11.3- 5

  6. Objective 2 Solve quadratic equations by using the quadratic formula. Slide 11.3- 6

  7. The solution set is CLASSROOM EXAMPLE 1 Using the Quadratic Formula (Rational Solutions) Solution: Solve a = 4, b = –11 and c = –3 Slide 11.3- 7

  8. The solution set is CLASSROOM EXAMPLE 2 Using the Quadratic Formula (Irrational Solutions) Solution: Solve a = 2, b = –14 and c = 19 Slide 11.3- 8

  9. 1. Every quadratic equation must be expressed in standard form ax2+bx+c=0 before we begin to solve it, whether we use factoring or the quadratic formula. 2. When writing solutions in lowest terms, be sure to FACTOR FIRST. Then divide out the common factor. CLASSROOM EXAMPLE 1 Solve quadratic equations by using the quadratic formula. Slide 11.3- 9

  10. The solution set is CLASSROOM EXAMPLE 3 Using the Quadratic Formula (Nonreal Complex Solutions) Solution: Solve a = 1, b = 4 and c = 5 Slide 11.3- 10

  11. Objective 3 Use the discriminant to determine the number and type of solutions. Slide 11.3- 11

  12. Use the discriminant to determine the number and type of solutions. Slide 11.3- 12

  13. CLASSROOM EXAMPLE 4 Using the Discriminant Find the discriminant. Use it to predict the number and type of solutions for each equation. Tell whether the equation can be solved by factoring or whether the quadratic formula should be used. a = 10, b = –1, c = –2 Solution: There will be two rational solutions, and the equation can be solved by factoring. Slide 11.3- 13

  14. CLASSROOM EXAMPLE 4 Using the Discriminant (cont’d) Find each discriminant. Use it to predict the number and type of solutions for each equation. Tell whether the equation can be solved by factoring or whether the quadratic formula should be used. Solution: a = 16, b = –40, c = 25 There will be two irrational solutions. Solve by using the quadratic formula. There will be one rational solution. Solve by factoring. Slide 11.3- 15

  15. CLASSROOM EXAMPLE 5 Using the Discriminant Find k so that the equation will have exactly one rational solution. x2 – kx + 64 = 0 Solution: There will be only on rational solution if k = 16 or k = 16. Slide 11.3- 16

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