(a) Write \(x^2 + 8x + 3\) in the form \((x + a)^2 - b\). [3]
(b) Sketch the graph of \(y = x^2 + 8x + 3\). Show clearly the coordinates of any turning points and the \(y\)-intercept.
[4]
Mark scheme (a)
Answer
Marks
Part marks and guidance
\((x + 4)^2 - 13\) final answer
3
B1 for \((x + 4)^2\)
B2FT for [+] 3 – their (a)\(^2\) after \((x +\) their \(a)^2\) correctly evaluated or B1 for [+] 3 – their \(a^2\) shown
If 0 scored, SC2 for final answer \((x + 4) - 13\)
FT can be implied eg \((x + 2)^2 - 1\) gets B2FT
Mark scheme (b)
Answer
Marks
Part marks and guidance
U shaped parabola with minimum value indicated in 3rd quadrant at (–4, –13) and intercepts positive \(y\) – axis at 3
4
FT U-shaped parabola with turning point at their \((-a, -b)\) from part (a) dep on answer of form \((x + a)^2 - b\) where \(a \ne 4\) and/or \(b \ne 13\)
Be generous for the U shape condone broken line TP values must be shown but could be marked on axes. Mark intention Sketch takes priority when marking Accept turning point = (– 4, –13) written in working or in table provided no contradiction on sketch
B1 for U shape curve B1 for their curve or line intercepts positive \(y\) – axis at 3
Must be stated on graph, 3 or (0, 3) Do not accept just in a table
B1 for turning point at \((-4, k)\) 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 \((k, -13)\) or FT for turning point at \((k, -b)\) dep on answer of form \((x + a)^2 - b\) in part (a)
If point (– 4, –13) only plotted on graph and no sketch then can score these final 2 marks
