(a) Write \(x^2 - 10x + 22\) in the form \((x - a)^2 - b\). [3]
(b) Sketch the graph of \(y = x^2 - 10x + 22\). Show clearly the coordinates of any turning points and the value of the \(y\)-intercept.[4]
Mark scheme (a)
Answer
Marks
Part marks and guidance
\((x - 5)^2 - 3\) final answer
3
B1 for \((x - 5)^2\) B2 FT for – 3 or M1 for \(22 - (-5)^2\) oe
M1 FT \(22 - (\textit{their}\ {-5})^2\) oe
Mark scheme (b)
Answer
Marks
Part marks and guidance
Correct sketch with TP at (5, −3) in 4th quadrant and \(y\) – intercept at (0, 22)
4
FT their (a) for TP M1 for U shaped curve B2FTdeptheir (a)for TP at (5, –3) in correct quadrant or B1FTdep for turning point at (\(k\), –3) or (5, \(k\)) soi FT for B2 or B1 dep on answer of form \((x - a)^2 - b\) in part (a), \(a, b \ne 0\)
B1 for \(y\) – intercept at 22 indicated
Be generous for the U shape condone broken line Values for \(y\) - intercept and TP must be shown but could be marked on axes. Mark intention Accept turning point = (5, –3)FT written in working provided no contradiction on sketch If point (5, –3)FT only plotted on graph in 4th quadrant and no sketch then B2 only
