An arithmetic progression has first term 5 and common difference $$\(d\)$$, where $$\(d> 0\)$$. The second, fifth and eleventh terms of the arithmetic progression, in that order, are the first three terms of a geometric progression. The graph of $$\(y=\mathrm{f}(x)\)$$ is transformed to the graph of $$\(y=\mathrm{h}(x)\)$$ by a reflection in one of the axes followed by a translation. It is given that the graph of $$\(y=\mathrm{h}(x)\)$$ has a minimum point at the origin. Give details of the reflection and translation involved. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . The function g is defined by $$\(\mathrm{g}(x)=3+6 x-2 x^{2}\)$$ for $$\(x \leqslant 0\)$$.

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