# Add Maths 2012 May-June Paper 21 23 Q12

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.
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 $$f ^{-1}$$.