Add Maths 2012 May-June Paper 21 23 Q12

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The equation of a curve is \(\quad y=2 x^{2}-20 x+37\).

  1. Express \(y\) in the form \(a(x+b)^{2}+c,\) where \(a, b\) and \(c\) are integers.
  2. Write down the coordinates of the stationary point on the curve.

A function \(f\) is defined by \(f : x \mapsto 2 x^{2}-20 x+37\) for \(x>k\). Given that the function \(f ^{-1}(x)\) exists,

  1. write down the least possible value of \(k\),
  2. sketch the graphs of \(y= f (x)\) and \(y= f ^{-1}(x)\) on the axes provided,
  3. obtain an expression for \(f ^{-1}\).

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