O-LevelAdditional MathematicsQuadratic functions4037/21 · May/June 2016 · Q68 Marks

Express 4x² + 8x - 5 in the form p(x+q)² + r, where p, q and r are constants to be found.

(i)Express 4x² + 8x - 5 in the form p(x+q)² + r, where p, q and r are constants to be found.[3]
(ii)State the coordinates of the vertex of y = |4x² + 8x - 5|.[2]
(iii)On the axes below, sketch the graph of y = |4x² + 8x – 5|, showing the coordinates of the points where the curve meets the axes. [Figure 6(iii) showing empty axes labelled y and x with origin O][3]

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Mark scheme

Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.

[B3,2,1,0] 4(x+1)²-9 one mark for each of p, q, r correct in a correctly formatted expression; allow correct equivalent values; If B0 then SC2 for 4(x+1)-9 or SC1 for correct 3 values seen in incorrect format e.g. 4(x+1x)-9 or 4(x²+1)-9 or for a correct completed square form of the original expression in a different but correct format. e.g. 2(√2x+√2)² -9
[B2FT] (-1, 9) B1FT (-q, -r) r < 0 for each correct coordinate
[B1] Correct symmetric W shape with cusps on x-axis
[B1] y-intercept marked at 5 only or coords indicated on graph
[B1] x-intercepts marked at -2.5 and 0.5 only x-axis or coords indicated on graph or close by

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