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 ax
^{2}+ 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. ax
^{2}+ 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. ax
- Using discriminant (b
^{2}– 4ac) to find the conditions where a quadratic equation has:- no real roots ==> b
^{2}– 4ac < 0 - 2 distinct real roots ==> b
^{2}– 4ac > 0 - equal roots ==> b
^{2}– 4ac = 0

- no real roots ==> b
- Using discriminant (b
^{2}– 4ac) to find the conditions where a line is:- tangent to a quadratic curve ==> b
^{2}– 4ac > 0 - cuts a quadratic curve at 2 distinct points ==> b
^{2}– 4ac > 0 - does not intersect the quadratic curve ==> b
^{2}– 4ac < 0

- tangent to a quadratic curve ==> b
- 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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