Functions $f$ and $g$ are each defined for $x \in \mathbb{R}$, and they are given by $f(x) = x^2 - 2x + 5$, $g(x) = x^2 + 4x + 13$.
(a)[4]
After first rewriting each of $f(x)$ and $g(x)$ in completed square form, express $g(x)$ in the form $f(x + p) + q$, where $p$ and $q$ are constants.
(b)[2]
Describe in full the transformation that maps the graph of $y = f(x)$ onto the graph of $y = g(x)$.
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This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Writes $f(x)=(x-1)^2+4$” …
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