O-LevelAdditional MathematicsQuadratic functions4037/21 · May/June 2018 · Q99 Marks

Express 5x² - 14x - 3 in the form p(x+q)² + r, where p, q and r are constants.

(i)Express 5x² - 14x - 3 in the form p(x+q)² + r, where p, q and r are constants.[3]
(ii)Sketch the graph of y = |5x² - 14x - 3| on the axes below. Show clearly any points where your graph meets the coordinate axes.[4]
(iii)State the set of values of k for which |5x² - 14x - 3| = k has exactly four solutions.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

[3] (i) 5(x-7/5)² - 64/5
[1] (i) B1 for each of p, q, r correct in correct format; allow correct equivalent values.
[1] (i) If B0, then SC2 for 5(x-7/5)² - 64/5 or SC1 for correct values but incorrect format
[4] (ii) B2 for fully correct shape in correct position or B1 for fully correct shape translated parallel to the x-axis
[1] (ii) B1 for y-intercept at (0, 3) marked on graph
[1] (ii) B1 for roots marked on graph at -0.2 and 3
[2] (iii) 0 < k < their (64/5)
[1] (iii) FT their (i) B1 for any inequality using their 64/5 or max y value is their 12.8soi

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