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.
   
   (Answer)

   $\begin{aligned} y &=2 x^{2}-20 x+37 \\ &=2\left(x^{2}-10 x\right)+37 \\ &=2\left(x^{2}-5 x-5 x+5^{2}-5^{2}\right)+37 \\ &\left.=2\left[(x-5)^{2}-25\right]+37\right] \\ &\left.=2(x-5)^{2}-50+37\right] \\ &=2(x-5)^{2}-13 \end{aligned}$
2. Write down the coordinates of the stationary point on the curve.
   
   (Answer)

   Coordinate of the stationary point= (5,-13)
   

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 $f ^{-1}$.