MYP Maths: Quadratic Functions & Parabolas FAQ

MYP 4-5 students need to graph parabolas from standard, factored and vertex form, identify the vertex, axis of symmetry, intercepts and turning point, and connect these features to real contexts like projectile motion or profit models. You'll also solve quadratics by factorising, completing the square and using the formula.

Standard form is $y=a{x}^2+bx+c$ and shows the y-intercept directly, while vertex form is $y=a(x-h{)}^2+k$ and reveals the turning point $(h,k)$ instantly. Neither form is 'better' — you pick whichever gives you the feature the question is actually asking for.

The axis of symmetry for $y=a{x}^2+bx+c$ is the vertical line $x=-\frac{b}{2a}$. It always passes through the vertex, so once you've calculated it you also know the x-coordinate of the turning point — plug it back in to get the y-coordinate.

Use $x=-\frac{b}{2a}$ to get the x-coordinate, then substitute it back into the original equation for the y-coordinate. If the equation's already in vertex form $y=a(x-h{)}^2+k$, the vertex is simply $(h,k)$ — no calculation needed.

The single biggest mistake I see marking mock papers is forgetting the negative sign in $x=-\frac{b}{2a}$, which flips the axis of symmetry to the wrong side of the y-axis. The second most common: sketching a parabola opening the wrong way because they ignored the sign of $a$.

Find the vertex, the axis of symmetry, and the y-intercept (set $x=0$), then plot the mirror point of the y-intercept across the axis of symmetry. Four points and a smooth curve is usually enough for full marks on a sketch question.

Quadratics are usually assessed under Criterion A (Knowing and Understanding) for algebraic manipulation and Criterion D (Applying mathematics in real-life contexts) when a task asks you to model something like a ball's trajectory or a company's revenue curve. Some units also touch Criterion B if you're asked to investigate patterns in coefficients.

Expect 'sketch', 'determine', 'solve', 'justify' and 'hence' most often. 'Sketch' wants labelled key features (vertex, intercepts) but not a perfectly scaled graph; 'hence' means you must use your previous answer, not start the method again from scratch.

MYP 4-5 quadratics is the direct foundation for DP Maths AA and AI Topic 2 (functions), where you'll meet the same vertex form, discriminant and graphing skills applied to harder modelling and, in AA, calculus. Students who are shaky on completing the square in MYP tend to struggle with DP function transformations.

MYP 5 is harder — it extends MYP 4's graphing and factorising into real-world modelling tasks, the discriminant, and connecting quadratics to simultaneous equations. MYP 4 focuses on building fluency with the three forms; MYP 5 expects you to apply that fluency under exam-style conditions.

Look for topical practice with worked solutions rather than a textbook alone — repetition on converting between forms and sketching is what actually builds speed. On RevisionPrep, the MYP Mathematics question bank and Topical Worksheets are organised by exactly this kind of sub-skill, so your child can drill vertex form or factorising specifically instead of a whole mixed chapter.

Ask your child to explain which form of a quadratic they'd pick for a given question and why — if they can't justify the choice, that's the actual gap, not just 'needing more practice'. Most students who struggle here haven't secured completing the square, and that one skill unlocks vertex form, the formula and graphing all at once.