Quadratic Functions, Key Terms

SPM Additional Mathematics papers are set bilingually in Bahasa Melayu and English, so knowing each Quadratic Functions term in both languages, and its precise meaning, protects you whichever way a question is phrased. Below are the key terms for this chapter, each shown in English, Malay and Chinese with a short definition.

Learn them until you can not only recall each term but use it correctly inside a full solution, because stating the right definition or condition in your working can itself earn a method mark.

• Quadratic Equation (Quadratic Equation · Persamaan Kuadratik · 二次方程), 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 (Discriminant · Pembeza · 判别式), 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 · Penyempurnaan Kuasa Dua · 配方法), 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 (Roots of a Quadratic Equation · Punca Persamaan Kuadratik · 二次方程的根), 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 (Axis of Symmetry · Paksi Simetri · 对称轴), 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 (Vertex Form · Bentuk Verteks · 顶点式), 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 (Quadratic Inequality · Ketaksamaan Kuadratik · 二次不等式), 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. →

Command words and technical terms are where careful reading turns into marks. When a question says "hence", it wants the previous result; "show that" wants the reasoning, not just the answer; "sketch" wants key features labelled, not a precise plot.

Combine that with the terms above and you can decode exactly what any Quadratic Functions question is asking before you start, which is half the battle.

Vocabulary is easiest to remember when it is tied to doing, not just reading. Rather than memorising the Quadratic Functions terms as a list, meet each one inside a worked question: when you use the word "gradient", "domain" or "coefficient" while actually solving a problem, its meaning fixes itself far more firmly than any flashcard.

A good habit is to say the step out loud in words as you write it,"I differentiate to get the gradient function, then substitute x to find the gradient at this point", because a term you can use in a sentence is a term you understand. Since the SPM paper is bilingual, it also helps to glance at the Malay and English versions of each term side by side once, so that whichever language a question is set in, the wording never throws you.

If a term still feels slippery, that usually points to the underlying idea needing another look rather than the word itself, and that is a good thing to bring to a lesson.

Notes and practice take a student a long way, but Quadratic Functions is one of those chapters where a second pair of eyes makes the difference between "I sort of get it" and "I get it reliably". Working one-to-one, a teacher watches the working as it happens and catches the exact step where a solution goes wrong, a sign dropped here, a condition forgotten there, a formula used in the right place but the wrong way.

That is something a worked answer in a book can never do, because the mistake happens in the doing, not in the reading. Because Quadratic Functions builds on earlier chapters, a teacher can also spot when the real gap is not in Quadratic Functions at all but in a Form 4 skill it quietly assumes, and rebuild that first so the new material finally lands.

In every lesson the emphasis is the same: understand the idea, show the method, and make the working clear enough that it earns marks even on a day when the final answer slips. Lessons are one-to-one and online, in English, and the teacher shapes each session around exactly where your child is with Quadratic Functions, from rebuilding a shaky foundation to sharpening for an A+.

Because the teacher is working with one student and not thirty, the pace is set by understanding rather than by a scheme of work: an idea that clicks in five minutes is not laboured, and one that does not is given the time it needs instead of being left behind for the class to move on.

None of this replaces the notes, examples and practice on this site, it makes them work harder. A student who has read the Quadratic Functions notes and tried the practice arrives at a lesson with real questions instead of a blank page, and an hour of teaching aimed at those questions is worth far more than an hour spent explaining what a textbook already says.

That is how we like students to use both together: study the material here, notice where it stops making sense, and bring exactly that to a teacher who can close the gap for good.