2025 ESSS P1 Q6

2025 ESSS P1 Q6

Secondary 4
4 marks
  1. Show that \(\mathrm{f}(x)=2x^2-6x-10\) can be written as \(\mathrm{f}(x)=a(x-b)^2+c\), where \(a\), \(b\) and \(c\) are constants to be found.[2]
  2. Hence, find the co-ordinates of the minimum point.[1]
  3. Determine if the curve lie completely above or below the \(x\)-axis or otherwise. Explain your answer.[1]

Solution:

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Answer:(a) \(a=2,\ b=\dfrac32,\ c=-\dfrac{29}2\). (b) \(\left(\dfrac32,-\dfrac{29}2\right)\). (c) Neither; it crosses the \(x\)-axis twice.

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