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Summary Notes for Quadratic Functions – O Level Add Math

Summary of quadratic functions for O level add math

Here, you’ll find a summary of what’s tested in the Quadratic function for O Level Additional Mathematics. If you are interested to know what’s in the syllabus for quadratic functions, I gave details in this post here.


Quadratic function is one of the first few topics students learn in O Level Additional Mathematics. This topic revolves around the quadratic expression ax2 + bx +c, its graph, finding the number of solutions (when it’s an equation), and solving it as an inequality. Solving quadratic equations is something that you learned in elementary Mathematics, and is assumed knowledge for this chapter. 

Summary of Quadratic Functions for O Level Add Maths

So now, let’s summarize the concepts for quadratic functions:

  •  Completing the square:
    • this involves manipulating the equation from ax2+bx+c into a(x+h)2 + g
    • if a >0, the curve has minimum point with coordinates (-h, g)
    • if a<0, the curve has a maximum point with coordinates (-h, g)
  • Discriminant of quadratic functions: b2 – 4ac
    • value of discriminant determines the number of real distinct roots of a quadratic equation
    • if  b2 – 4ac > 0, there are 2 distinct real roots
    • if  b2 – 4ac = 0, there are equal real roots
    • if  b2 – 4ac < 0, there are no real roots
  • If you have a curve of the equation, y = f(x), and a line of equation y = g(x), you’ll first need to equate f(x) to g(x) and manipulate it until it becomes the form ax2+bx+c (if you can’t make it is not a quadratic form, then it’s not a discriminant question)
    • if  b2 – 4ac > 0, line cuts curve at 2 distinct point
    • if  b2 – 4ac = 0, line is a tangent to the curve
    • if  b2 – 4ac < 0, line and curve do not intersect
  • Solving quadratic inequality
    • To solve quadratic inequality, you’ll need to make one side of the inequality sign 0, and factorize the other size.
    • Sketch the curve and determine which section is needed (> 0 or < 0) and from there determine the inequality
  • Solving non-linear simultaneous equations

Want to learn more about Quadratic Functions for O Level Add Maths?

Mathematics is all about applying and being able to do questions. Apart from knowing these notes and concepts, you must also be familiar with how to apply them to the questions. The nice thing about Additional Mathematics is the questions are quite standard.  In my course, I go into detail not only the concepts but how to apply them. We also go through many questions together step-by-step, so that students finish the course equipped with the skills needed to tackle their test and exam questions on quadratic function with confidence. I also included a revision on solving quadratic function (an assumed knowledge for Add Math) in my course, so if you need a revision, you can go through the lectures. You can purchase the course instantly on Udemy, and watch and learn instantly. Get the course on Quadratic Functions here. 

Quadratic function course for O Level Additional Mathematics
https://www.udemy.com/course/quadratic-functions/?referralCode=37E5800DA81C1DBD188A