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 results from completing the square i.e. ax2 + bx + c = a(x+h)2 + g
- 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
I give tips on how to complete the square of quadratic functions quickly. This is only available in my course on Udemy. I also go through the steps on how to approach questions in this chapter. So if you want a detailed course, definitely check out our Complete Course on quadratic functions.
Get our complete on-demand video course on quadratic functions here.

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