Quadratic Functions and Equations in One Variable · Form 4
What is a quadratic function?
A quadratic function is any function that can be written as f(x) = ax² + bx + c with a ≠ 0, and its graph is always a smooth U-shaped curve called a parabola.
The highest power is two
A quadratic function has an x² term and nothing higher, written f(x) = ax² + bx + c where a, b and c are numbers and a is not zero. That single squared term is what bends the graph into a curve.
If a were zero the x² term would disappear and you would be left with a straight line, which is a linear function, not a quadratic.
Its graph is a parabola
Every quadratic draws the same family of smooth U-shaped curve, called a parabola. When a is positive the curve opens upward and has a lowest point; when a is negative it opens downward and has a highest point.
That lowest or highest point is the turning point, and the parabola is a mirror image on either side of the vertical line running through it.
Reading it before you draw
You can tell a lot from the equation alone. The constant c is where the curve crosses the y-axis, found by putting x = 0, and the sign of a tells you which way it opens.
A common mistake is to expect a parabola to be pointed like a V, it is always rounded and smooth and never has a corner. Another is to assume the curve must cross the x-axis, when some parabolas sit entirely above or below it.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
Why must a ≠ 0 in f(x) = ax² + bx + c?
If a = 0, the x² term disappears and the function becomes linear, f(x) = bx + c, no longer quadratic. Exam questions sometimes disguise this by giving an equation that only becomes quadratic after expanding brackets, so always check the x² coefficient survives before answering.
How can you tell an equation is quadratic even if it doesn't show x² directly?
Expand or simplify first, brackets like (x + 1)(x − 2) = 3, or a fraction cross-multiplied, can hide an x² term that only appears after working. A common Paper 1 trap is picking "linear" too quickly; always simplify fully before deciding the equation's degree.
Does every quadratic graph open the same way?
No, the sign of a decides the direction: a > 0 opens upward with a minimum point, a < 0 opens downward with a maximum point. A common mix-up is thinking c controls the opening direction; c only shifts the graph vertically, it never flips it.