Quadratic Functions, Glossary

Knowing the vocabulary of Quadratic Functions precisely is worth easy marks in SPM Add Math. Questions often turn on a single keyword, read it correctly and the method follows; misread it and even good algebra earns nothing.

Because the SPM paper is bilingual (BM/EN), each term below shows the English and Malay wording, so your child recognises it whichever way a question is phrased.

• Quadratic Equation, A quadratic equation has the general form $ax^{2}+bx+c=0$ with $a\neq 0$. Its highest power is two, so it can have up to two roots. We solve it by factorising, completing the square, or using the formula $x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$. →
• Discriminant, The discriminant is the expression $b^{2}-4ac$ taken from a quadratic equation $ax^{2}+bx+c=0$. Its sign reveals the type of roots without solving: positive gives two distinct real roots, zero gives two equal roots, and negative gives no real roots. →
• Completing the Square, Completing the square rewrites a quadratic $ax^{2}+bx+c$ in the form $a(x+p)^{2}+q$. It works by forming a perfect square from the $x$-terms and adjusting the constant. This method reveals the maximum or minimum point directly and can solve any quadratic equation. →
• Roots of a Quadratic Equation, The roots of a quadratic equation are the values of $x$ that make it equal to zero; graphically they are where the curve crosses the x-axis. For $ax^{2}+bx+c=0$, the sum of roots is $-\frac{b}{a}$ and the product is $\frac{c}{a}$, which helps form equations from given roots. →
• Axis of Symmetry, The axis of symmetry is the vertical line that divides a parabola into two mirror-image halves and passes through its vertex. For $y=ax^{2}+bx+c$ its equation is $x=-\frac{b}{2a}$. Points at equal horizontal distances from this line share the same $y$-value. →
• Vertex Form, The vertex form of a quadratic function is $f(x)=a(x-h)^{2}+k$, where $(h,k)$ is the vertex, the turning point of the parabola. The value of $a$ controls the width and direction, while $h$ and $k$ shift the graph horizontally and vertically. It shows the maximum or minimum at a glance. →
• Quadratic Inequality, A quadratic inequality compares a quadratic expression with zero, such as $x^{2}-x-6>0$. We solve it by finding the roots, then testing which regions of the number line satisfy the inequality. A sketch of the parabola or a number line makes the correct range of $x$ clear. →

Do not just memorise definitions, practise using each term inside a full solution, the way a marker expects to see it. In the Quadratic Functions chapter especially, stating the right definition or condition in your working can itself earn a method mark.

Our teachers check that a student can both recall a term and deploy it fluently under exam conditions.

Vocabulary sticks best when it is tied to doing rather than reading. Instead of learning the Quadratic Functions terms as a flat list, meet each one inside a worked question and say the step aloud in words as you write it, a term you can use in a sentence is a term you understand.

It also helps to link related terms together rather than in isolation, since Quadratic Functions questions usually combine several ideas at once. Because the SPM paper is bilingual, glance once at the Malay and English wording of each term side by side, so the language a question is set in never throws you.

If a term keeps feeling slippery, that is usually a sign the underlying idea needs another look, not the word itself, and that is exactly the kind of gap a one-to-one lesson closes quickly.