Topic Brief: Quadratic Functions

Provenance: compiled 2026-09-29. Source is research/veridian/WMA11-verified-facts.md (the primary, provenance-checked source, searched directly for this topic — no fresh PDF extraction was done for this document), cross-checked against signal-frequency-and-boundaries.md §1, codex-formula-and-method-bank.md §1.1.3/§2.1.1, forge-exam-technique-guide.md §2.2, the lesson file content/veridian/curriculum/wma11/quadratic-functions.ts, and content/veridian/question-bank/wma11.ts — this brief deliberately does not restate anything those five documents already cover. Not affiliated with or endorsed by Pearson Edexcel.

#SIGNAL Topic Master Brief — Quadratic Functions (spec 1.3, 1.5)

#Scope: what this covers, and what it doesn't

This brief is about the core skills of spec 1.3 (quadratic graphs, turning points) and 1.5 (completing the square; solving quadratics by factorisation, formula, or completing the square) — tested as the actual point of a question, not as a step buried inside a different one. Three close relatives already have their own documents in this hub and are not repeated here: the discriminant with a parameter (spec 1.4) has its own SIGNAL brief; quadratic/reciprocal inequalities interpreted graphically (spec 1.7–1.9) and "hidden quadratic" substitution (spec 1.1/1.5/1.6) each have their own lesson file. If a question hides a quadratic inside a fraction, an exponential substitution, or an inequality, that's covered elsewhere — this brief is about quadratic-function knowledge tested directly.

#Frequency: seen in 0 of 5 series checked as a standalone question — one further sighting outside that base

The facts bank fully mined five WMA11 examiner reports question-by-question: Jan 2019, Oct 2020, Oct 2021, Jan 2023, Jan 2025. None of the five contains a question whose entire point is core spec 1.3/1.5 content on its own — sketching a quadratic, finding a turning point by completing the square from a given f(x), or solving a bare quadratic as the whole task. That mechanical skill (solving a three-term quadratic) instead turns up constantly as an embedded sub-step inside other question types — discriminant-with-a-parameter questions, hidden-substitution questions, simultaneous-equations questions — which is real, but is already documented under those topics' own entries, not this one's to re-claim.

One further sighting exists outside that five-series base: June 2022 Q5(a), found by a single targeted-question read of that series (not a full-paper read, so June 2022's coverage of every other question is unknown). Two more series, Oct 2022 and Jan 2024, are confirmed as genuine mark schemes but were never mined question-by-question, so this topic's presence or absence in them is simply unread, not absent.

#The one confirmed appearance

June 2022 Q5(a) (WMA11_01_2206_MS, part (a) of a 9-mark question, 4 marks): "The curve C has equation y = f(x). Given that f(x) is a quadratic expression, the maximum turning point on C has coordinates (−2, 12), C cuts the negative x-axis at −5, find f(x)." Real mark scheme: M1 (a quadratic form built from two given pieces of information — vertex form, factorised form, or general form) → A1 (equation set up with the unknown constants included, not with the leading multiplier assumed to be ±1) → dM1 (a full method for the remaining constant) → A1 (the correct equation, any equivalent form). Parts (b)–(c) of the same question were not read in this pass and remain unverified here.

This is the reverse of the far more routine skill: instead of starting from a known f(x) and finding the turning point, the question starts from the turning point plus one other point and reconstructs the unknown f(x) — with the leading multiplier as a genuine unknown to solve for, not assumed.

#Mark-tariff pattern and recurring angle: one data point, honestly labelled

With a single confirmed sighting, no pattern can honestly be claimed across series. What's real: this instance carried 4 marks and sat as the opening part of a larger 9-mark question — treat that as one data point, not a tariff rule. Likewise, no "recurring angle" can be asserted from one sighting; the one context found is a word-described curve (turning point plus an x-intercept, leading multiplier unknown), and whether that's the paper's habitual framing for this skill or a one-off is not yet known.

What the one sighting does support, because it's a direct examiner-report quote rather than an inference, is the trap's severity: "Most candidates knew the correct quadratic form but failed to achieve a correct answer due to ignoring the multiplier k... As a result 1 out of 4 was a very common score," and "only a minority of candidates achieved full marks." That's a real, quoted, high-frequency failure on this one confirmed instance — worth flagging even from a single sighting.

#If this topic appears: what to expect

Two honestly-supported possibilities, not one. Most of this topic's real exam presence, per the fully-read record, is as an unlabelled sub-step inside a differently-titled question (discriminant, hidden-substitution, or simultaneous equations — see those documents for the traps that actually apply there). Less commonly — one confirmed instance — it can be asked directly, as a reverse-reconstruction question, early in a longer multi-part item. If it is asked that way, the single most damaging, examiner-documented error is naming the right quadratic shape (vertex form, factorised form, general form) from the turning point and root, then never solving for the leading multiplier at all — worth checking for explicitly before moving on.