Moderate -0.8 This question tests basic differentiation of a quadratic and understanding of horizontal translations. Part (i) requires differentiating (x-a)² to get 2(x-a), then equating to 2x-6 to find a=3. Part (ii) asks for a simple translation description. Both parts are routine applications of standard C1 techniques with no problem-solving insight required, making it easier than average.
The curve \(C\) has the equation \(y = (x - a)^2\) where \(a\) is a constant.
Given that
$$\frac{dy}{dx} = 2x - 6,$$
\begin{enumerate}[label=(\roman*)]
\item find the value of \(a\), [4]
\item describe fully a single transformation that would map \(C\) onto the graph of \(y = x^2\). [2]
The curve $C$ has the equation $y = (x - a)^2$ where $a$ is a constant.
Given that
$$\frac{dy}{dx} = 2x - 6,$$
\begin{enumerate}[label=(\roman*)]
\item find the value of $a$, [4]
\item describe fully a single transformation that would map $C$ onto the graph of $y = x^2$. [2]
</enumerate}
\hfill \mbox{\textit{OCR C1 Q4 [6]}}