Minimum or maximum of a quadratic at its vertex

CAT has tested this idea 4 times across 4 papers, from 2020 to 2025. Solve one, and the others are the same method with different numbers or wording, which is why repeated concepts are the most efficient thing to practise.

Question	What it asks	Answer
CAT 2025 Slot 1 · QA Q8	min of one quadratic exceeds max of another	D
CAT 2021 Slot 3 · QA Q22	minimum of f(g(x)) − 3x	D
CAT 2022 Slot 2 · QA Q20	non-negative quadratic with f(2) = 0 has vertex at 2	C
CAT 2020 Slot 2 · QA Q14	f ≥ 0 for all x; smallest b	C

Part of Functions & Graphs (23 questions since 2017).