2023 YTSS P2 Q3

2023 YTSS P2 Q3

Secondary 4
5 marks
  1. Show that \(\mathrm f(x)=3x^2-9x+7\) can be written as \(\mathrm f(x)=a(x-b)^2+c\), where \(a\), \(b\) and \(c\) are constants to be found.[4]
  2. Hence, explain why the function \(\mathrm f(x)\) is always positive.[1]

Solution:

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Answer:(a) \(3(x-\dfrac32)^2+\dfrac14\). (b) \(\mathrm f(x)\ge\dfrac14>0\).

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