Moderate -0.3 This is a standard C1 completing the square question with routine sketching and distance calculation. Part (i) is textbook completing the square, part (ii) is direct application of the result, and part (iii) requires finding roots using the quadratic formula and calculating distance—all standard techniques with no novel insight required. Slightly easier than average due to being highly procedural.
Express \(3x^2 - 12x + 11\) in the form \(a(x + b)^2 + c\). [4]
Sketch the curve with equation \(y = 3x^2 - 12x + 11\), showing the coordinates of the minimum point of the curve. [3]
Given that the curve \(y = 3x^2 - 12x + 11\) crosses the \(x\)-axis at the points \(A\) and \(B\),
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item find the length \(AB\) in the form \(k\sqrt{3}\). [5]
\begin{enumerate}[label=(\roman*)]
\item Express $3x^2 - 12x + 11$ in the form $a(x + b)^2 + c$. [4]
\item Sketch the curve with equation $y = 3x^2 - 12x + 11$, showing the coordinates of the minimum point of the curve. [3]
\end{enumerate}
Given that the curve $y = 3x^2 - 12x + 11$ crosses the $x$-axis at the points $A$ and $B$,
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item find the length $AB$ in the form $k\sqrt{3}$. [5]
</enumerate}
\hfill \mbox{\textit{OCR C1 Q8 [12]}}