Quadratic Functions and Equations in One Variable · 1.1.1
Quadratic expressions
A quadratic expression in one variable, such as x, has the general form ax² + bx + c, where a, b, c are constants and a ≠ 0. This standard asks students to recognise such expressions, identify that the highest power is 2, and distinguish them from linear or cubic expressions.
The official learning standard (1.1.1)
“Identify and describe the characteristics of quadratic expressions in one variable.”
What it means
A quadratic expression in one variable, such as x, has the general form ax² + bx + c, where a, b, c are constants and a ≠ 0. This standard asks students to recognise such expressions, identify that the highest power is 2, and distinguish them from linear or cubic expressions.
How it is examined
In Paper 1, students are given several expressions and must pick out or justify which ones are quadratic in one variable, testing understanding of degree 2 and the condition a ≠ 0. This idea also underlies later objective and subjective questions on quadratic equations and graphs.
Worked example
Determine whether each of the following is a quadratic expression in one variable. If not, state why.
(a) 2x² − 5x + 3 (b) 7x − 4 (c) x³ + 2x² − 1
- (a) The highest power of x is 2, and the coefficient of x² is 2 ≠ 0.
- (b) The highest power of x is 1 (there is no x² term), so this is a linear expression, not quadratic.
- (c) The highest power of x is 3 (from x³), so this is a cubic expression, not quadratic.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
What makes an expression quadratic instead of linear?
A quadratic expression must contain an x² term with a non-zero coefficient, this is what gives it degree 2. A linear expression only has terms up to x¹, with no x² term at all.
Can a quadratic expression have more than one variable?
This standard is limited to one variable, so an expression such as x² + xy + y² is outside its scope. In SPM Form 4 quadratic expressions, only a single variable like x is used, in the form ax² + bx + c.
Why must a ≠ 0 in ax² + bx + c?
If a = 0, the x² term disappears and the expression reduces to bx + c, which is linear (or a constant if b = 0 too). The condition a ≠ 0 is exactly what keeps the expression quadratic, degree 2.