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O-LevelAdditional MathematicsQuadratic functions4037/21 · May/June 2024 · Q24 Marks

Write 3+4x-2x² in the form a+b(x+c)², where a, b and c are integers.

  1. (a)Write 3+4x-2x² in the form a+b(x+c)², where a, b and c are integers.[3]
  2. (b)Hence write down the range of the function f(x) = 3+4x-2x², where x ∈R.[1]

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

  1. [B3] Mark final expression
  2. [B2] for –2(x – 1)²
  3. [B1] for (x – 1)² or b = –2, c = –1
  4. [B1] for 5 + b(x + c)² oe with numerical values of b and c or a = 5
  5. [B1] f ≤ their 5

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About this question

Topic
Quadratic functions, O-Level Additional Mathematics (syllabus 4037). Structured question, 4 marks.
Source
O-Level Additional Mathematics, May/June 2024 Paper 2 Variant 1, question 2.

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