Quadratic functions and equations connect algebra, graphs and real situations. This section has four lessons and a practice set, and belongs to the wider SPM Mathematics guide.
What does this section cover?
Begin with recognising a quadratic from its highest power, which teaches you to simplify before you decide. Then learn solving factorisable quadratic equations.
Next is finding roots from a quadratic graph. The last lesson covers interpreting a turning point in a contextual problem. The practice set mixes all four.
One function, four questions
Take the function y = x² − 6x + 8. Each lesson asks a different question about it.
| Question | Skill | Answer |
|---|---|---|
| Is it quadratic, and what are a, b, c? | Recognition | Yes, a = 1, b = −6, c = 8 |
| Solve x² − 6x + 8 = 0 | Factorising | (x − 2)(x − 4) = 0, so x = 2 or 4 |
| Where does the graph meet the x-axis? | Graph reading | At x = 2 and x = 4 |
| What is the lowest point? | Turning point | (3, −1), halfway between 2 and 4 |
The same two numbers, 2 and 4, answer the algebra and the graph questions. That link is what makes the topic manageable once you see it.
Who should start where?
If you are new to Form 4, begin at the recognition lesson and move in order. If you can factorise but lose marks on graphs, start at the third lesson.
If your marks fall on word problems, go straight to the turning point lesson, then return to the earlier ones only if the algebra breaks. Whatever your starting point, finish with the practice set and mark method and answer separately.
A quick algebra refresher, such as the algebra step repair trainer, helps if expanding brackets is the weak spot. A teacher can also help in online one-to-one Mathematics tuition.