Quadratic Functions and Equations in One Variable
Quadratic function
A function of the form y = ax² + bx + c, where a is not zero; its graph is a parabola.
| English | Quadratic function |
|---|---|
| Bahasa Melayu | Fungsi kuadratik |
| 中文 | 二次函数 |
How it is used
For y = 2x² − 4x + 1, this is a quadratic function because a = 2 ≠ 0; substituting x = 3 gives y = 2(9) − 12 + 1 = 7, a point (3, 7) on its parabola.
Where it shows up in SPM
The core object of the Quadratic Functions and Equations chapter (Form 4). In Paper 1 you identify a, b, c or read graph features; in Paper 2 you sketch the graph, find the turning point by completing the square, and state the range of x for which y is positive or negative.
Don't confuse it with
Open the chapter: Quadratic Functions and Equations in One Variable →
Frequently asked questions
Why must a not equal zero?
If a = 0 the x² term vanishes and you are left with y = bx + c, a straight line, not a parabola. The a ≠ 0 condition is exactly what makes the function quadratic and gives it its curved, U-shaped graph.
How is a quadratic function different from a quadratic equation?
A function y = ax² + bx + c gives a y-value for every x and draws a whole curve. An equation ax² + bx + c = 0 asks for the specific x-values where y = 0, which are the roots where the curve meets the x-axis.
What does the sign of a tell me?
The sign of a decides the shape. When a is positive the parabola opens upward and has a minimum point; when a is negative it opens downward and has a maximum point.
A larger |a| makes the curve narrower.