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Note 3: Solving Quadratics

Note 3: Solving Quadratics. Note 3: Solving Quadratics. Methods for solving quadratics: Factorising Completing the square Using the quadratic formula Graphics calculator. Method A: Factorising Set equation equal to 0 Factorise Set each factor to zero and solve Examples:

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Note 3: Solving Quadratics

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  1. Note 3: Solving Quadratics

  2. Note 3: Solving Quadratics Methods for solving quadratics: • Factorising • Completing the square • Using the quadratic formula • Graphics calculator

  3. Method A: Factorising • Set equation equal to 0 • Factorise • Set each factor to zero and solve Examples: 1. 5x2 + 20x = 0 5x(x + 4) = 0 x = 0 or x = -4 2. 2x2 + 2x = 24 2x2 + 2x – 24 = 0 Make = 0 2(x2 + x – 12) = 0 2(x – 3)(x + 4) = 0 Factorise x = 3 or x = -4 Page 163 Exercise 8D.1

  4. Method B: Completing the Square • Complete the Square • Solve Examples: 1. 5x2 + 20x = 0 5(x2 + 4x) = 0 x2 + 4x = 0 (x + 2)2 – 4 = 0 (x + 2)2 = 4 x + 2 = ± 2 So, x + 2 = 2 or x + 2 = -2 x = 0 or x = -4

  5. Page 167 Exercise 8D.2 Method B: Completing the Square • Complete the Square • Solve Examples: 2. 2x2 + 2x – 24 = 0 2(x2 + x - 12) = 0 x2 + x – 12 = 0 (x + ½ )2 – ¼ – 12 = 0 (x + ½ )2 = 12 ¼ x + ½ = ± 3.5 So, x + ½ = 3.5 or x + ½ = -3.5 x = 3 or x = -4

  6. Method C: Quadratic Formula If ax2 + bx + c = 0 then, Proof for this is page 168 Examples: 1. 5x2 + 20x = 0 a = 5, b = 20, c = 0 Therefore: x = 0 and x = -4

  7. Examples: 1. 2x2 + 2x – 24 = 0 a = 2, b = 2, c = -24 Therefore: x = 3 and x = -4

  8. Method D: Graphics Calculator • Use EQUA –POLYNOMIAL to solve • GRAPH equation – x intercepts • GRAPH equations – y intersections Examples: 1. 5x2 + 20x = 0 a = 5, b = 20, c = 0 Graph y = 5x2 + 20x

  9. Method D: Graphics Calculator • Use EQUA –POLYNOMIAL to solve • GRAPH equation – x intercepts • GRAPH equations – y intersections Examples: 2. 2x2 = -2x + 24 Plot y = 2x2 y = -2x + 24 Find Intersections (-4,32) and (3,18)

  10. Page 170 Exercise 8F

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