What you need to know for O Level for Quadratic Functions (O Level Add Maths)

In O Level Additional Mathematics, this is what you need to know for quadratic functions:

• Finding maximum and minimum of a quadratic function by completing the square
• i.e. converting ax² + bx + c to a(x+h)² + g

• Conditions for a quadratic function to be always positive or negative
  • Using results from completing the square i.e. ax² + bx + c = a(x+h)² + g
    • This occurs when a > 0 and g > 0
    • This occurs when  a < 0 and g < 0
•  Using discriminant (b²– 4ac) to find the conditions where a quadratic equation has:
  • no real roots ==> b²– 4ac < 0
  • 2 distinct real roots ==> b²– 4ac > 0
  • equal roots ==> b²– 4ac = 0
• Using discriminant (b²– 4ac) to find the conditions where a line is:
  • tangent to a quadratic curve ==> b²– 4ac > 0
  • cuts a quadratic curve at 2 distinct points ==> b²– 4ac > 0
  • does not intersect the quadratic curve ==> b²– 4ac < 0
• Solving simultaneous equations
  • This can be done using the substitution method (most commonly used) or the elimination method. 
• Solving quadratic inequalities

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