(a) Write \(x^2 - 6x + 11\) in the form \((x - a)^2 + b\). [3]
(b) Sketch the graph of \(y = x^2 - 6x + 11\). Show clearly the coordinates of any turning points.[3]
Mark scheme (a)
Answer
Marks
Part marks and guidance
\((x - 3)^2 + 2\) final answer
3
B1 for \((x - 3)^2\) B2 FT for 2
or M1 for \(11 - (\textit{their} -3)^2\) If 0 scored, SC2 for final answer \((x - 3) + 2\)
FT can be implied, check \(11 - (\textit{their} -3)^2\)
Mark scheme (b)
Answer
Marks
Part marks and guidance
U shaped parabola with minimum value indicated in 1st quadrant at (3, 2)
3
FT U-shaped parabola with turning point at their (– \(a\), \(b\)) from part (a) dep on answer of form \((x + a)^2 + b\) where \(a \ne -3\) and/or \(b \ne 2\)
B1 for U shape curve
B1 for turning point at (3, \(k\)) or FT for turning point at (–\(a\), \(k\)) dep on answer of form \((x + a)^2 + b\) in part (a) B1 for turning point at (\(k\), 2) or FT for turning point at (\(k\), \(b\)) dep on answer of form \((x + a)^2 + b\) in part (a)
Be generous for the U shape condone broken line Sketch takes priority when marking Do not allow all 3 marks if (3, 2) indicated on U shaped parabola but TP on sketch is in wrong quadrant Values must be shown but could be marked on axes. Mark intention Accept turning point = (3, 2) written in working provided no contradiction on sketch
If point (3, 2) only plotted on graph and no sketch then B0B1B1
Notes
(corrected from the printed mark scheme: the form of the part (a) answer is printed as \((x + a)^2 - b\) in three places; it is \((x + a)^2 + b\), matching the turning point (–\(a\), \(b\)) and the answer \((x - 3)^2 + 2\))
