The functions $f$ and $g$ are each defined for every $x \in \mathbb{R}$, and are given by $f(x) = x^2 - 4x + 9$ and $g(x) = 2x^2 + 4x + 12$.
(a)[1]
Express $f(x)$ in the form $(x-a)^2+b$.
(b)[2]
Express $g(x)$ in the form $2[(x + c)^2 + d]$, where $c$ and $d$ are constants.
(c)[1]
Express $g(x)$ in the form $k f(x + h)$, where $k$ and $h$ are integers.
(d)[4]
Describe fully the two transformations that have been combined to turn the graph of $y = f(x)$ into the graph of $y = g(x)$.
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This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Write the function as $(x-2)^2+5$.” …
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