2025 IGCSE Additional Mathematics February/March 0606/22 Q2

2025 IGCSE Additional Mathematics February/March 0606/22 Q2

9 marks
  1. Find the \(x\)-coordinates of the stationary points on the curve \(y=\dfrac12(3-2x)(x+2)^2\).[4]
  2. On the axes, sketch the graph of \(y=\dfrac12(3-2x)(x+2)^2\) stating the intercepts with the coordinate axes.[3]
  3. Find the values of \(k\) for which the equation \(\dfrac12(3-2x)(x+2)^2=k\) has three real and distinct roots.[2]

Solution:

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Answer:(a) \(x=-2,\dfrac13\) (b) Sketch shown; intercepts \((-2,0),(1.5,0),(0,6)\). (c) \(0<k<\dfrac{343}{54}\)

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