The Quadratic Formula

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  How to use the Quadratic Formula to solve quadratic equations

  ax² + bx + c = 0

  • a, b are coefficients

  {−b ± √(b² − 4ac)} ÷ 2a

  • Discriminant = b² − 4ac
    • Discriminant >0, Two real solutions
    • Discriminant = 0, One real solution
    • Discriminant < 1, No real solutions
      • Complex solutions

  Next target: Complex numbers

  The Distributive property

  Formulae/equations, changing the subject

  ~ Quadratics

  Derivation:

  ax² + bx + c = 0

  a(x² + ^b/_a + ^c/_a) = 0

  x² + ^b/_a + ^c/_a = 0

  Completing the square:

  (x + ^b/_2a)² − b²/4a² + ^c/_a = 0

  Solve for x:

  (x + ^b/_2a)² = b²/4a² − ^c/_a

  x + b/2a = ±√(b²/4a² − ^c/_a)

  x = −b/2a ± √(b² − 4a²c/a) ÷ 2a