Quadratic equations

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Quadratic equations

  1. 1. 1Jun 1­03:09 p.m.Quadratic equationsax2 +bx +c = 0by factorisationusing GDCby formulay = (x­2)2y = ­ x 2 + 1y = x2 ­ 2y = x2 + 3 y = (x ­ 3 )2+5y= ­ 2 x 2 + 1
  2. 2. 2May 29­06:50 p.m.y= 3x(x­2) y= ­x(x­2)y= x(x­2)y= (x­1)(x+2)y= 2(x­1)(x+2)
  3. 3. 3Jun 1­03:09 p.m. Quadratic EquationsBy the end of the lessson you will be able to  :• Solve quadratic equations by different methods.• Anticipate the number of solutions of a quadratic equation by studying its discriminant.
  4. 4. 4Jun 1­03:09 p.m.Quadratic equationsby factorisationusing GDCby formulaby completing the square
  5. 5. 5Jun 1­03:09 p.m.Solve the equation:  
  6. 6. 6Jun 1­03:09 p.m.Solve the equation:  
  7. 7. 7Jun 1­03:09 p.m.Solve the equation:
  8. 8. 8Jun 1­03:09 p.m.Use the quadratic formula to solve the equation:
  9. 9. 9Jun 1­03:09 p.m.Simplify and then use your GDC to solve the equation:
  10. 10. 10Jun 1­03:09 p.m.Use your GDC to solve the equations:
  11. 11. 11Jun 1­03:12 p.m.Unusual quadratic equations:
  12. 12. 12Jun 1­03:12 p.m.Unusual quadratic equations:
  13. 13. 13Jun 1­03:12 p.m.Disguised quadratic equations:
  14. 14. 14Jun 1­03:12 p.m.Unusual quadratic equations
  15. 15. 15Jun 1­03:12 p.m.Unusual quadratic equations:
  16. 16. 16Jun 1­03:10 p.m.The quantity is called thediscriminant of the quadratic equation.Δ > 0 ⇒ Δ = 0 ⇒ Δ < 0 ⇒ the equation has two real roots.the equation has a repeated root.the equation has no real roots.qformula.wma
  17. 17. 17Jun 1­03:11 p.m.Δ > 0    Δ = 0 Δ < 0 Two different  real rootsOne repeated root (or two equal roots)No   root.
  18. 18. 18Jun 1­03:11 p.m.Calculate the discriminant of the quadratic expression. Hence show thatis always positive.
  19. 19. 19Jun 1­03:12 p.m.Find the possible values of the constant k such that the equationhas a repeated root.
  20. 20. 20Jun 1­03:13 p.m.Solve the equation  
  21. 21. 21Jun 1­03:13 p.m.Solve the equation                             , for 0o  ≤  x   ≤ 360o
  22. 22. 22Jun 1­03:13 p.m. Find the maximum area of a rectangle which has aperimeter of 28 units.
  23. 23. Attachmentsqformula.wma

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