A-LevelMathematicsQuadratics9709/12 · Oct/Nov 2022 · Q69 Marks

The equation of a curve is y = 4x² + 20x + 6.

(a)Express the equation in the form y = a(x + b)² + c, where a, b and c are constants.[3]
(b)Hence solve the equation 4x² + 20x + 6 = 45.[3]
(c)Sketch the graph of y = 4x² + 20x + 6 showing the coordinates of the stationary point. You are not required to indicate where the curve crosses the x- and y-axes.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

B1 a = 4. There is no requirement for the candidate to list a, b and c. Look at values in their final expression, condone omission of ² , and award marks as follows: y = 4(x + 5/2)² - 19
B1 b = 5/2 OE
B1 c = -19
M1 Equate their quadratic completed square form from 6(a) to 45 or re-start and use completing the square. (Their 4 (x+5/2)² - 19) = 45 => (x + 5/2)² = 16
DM1 Any valid method leading to two answers. Solve as far as x =
A1 SC: If M0 or M1 DM0 awarded, B1 available for correct final answers. [x=] -5/2 ± 13/2 or x = 4 and x = -9
B1 No axes required, ignore any axes even if incorrect. Quadratic curve that is the right way up (must be seen either side of stationary point)
B1 FT FT their values from 6(a) as long as their expression is of the form p(qx+r)² +s. Expect (-5/2, -19). Stationary point stated using any valid method or correctly labelled on their diagram.
B1 FT Condone if stated correctly but plotted incorrectly.

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