2025 IGCSE Additional Mathematics October/November 0606/23 Q3

2025 IGCSE Additional Mathematics October/November 0606/23 Q3

9 marks
    1. Write \(x^2-x-6\) in the form \((x+a)^2+b\) where \(a\) and \(b\) are constants.[2]
    2. Hence write down the coordinates of the stationary point on the curve \(y=x^2-x-6\).[2]
  2. On the axes, draw the graph of \(y=|x^2-x-6|\) for \(-4\le x\le4\).[3]
  3. Use your graph to solve the inequality \(|x^2-x-6|<4\).[2]

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Answer:(a)(i) \((x-\tfrac12)^2-\tfrac{25}4\) (ii) \((\tfrac12,-\tfrac{25}4)\) (b) Graph shown. (c) \(-2.7<x<-1\) or \(2<x<3.7\), approximately.

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