A-LevelMathematicsQuadratics9709/12 · Oct/Nov 2013 · Q1010 Marks
A curve has equation y = 2x² – 3x.
- (i)Find the set of values of x for which y > 9.[3]
- (ii)Express 2x² – 3x in the form a(x + b)² + c, where a, b and c are constants, and state the coordinates of the vertex of the curve.[4]
- (iii)The functions f and g are defined for all real values of x by f(x) = 2x² – 3x and g(x) = 3x + k, where k is a constant. Find the value of k for which the equation gf(x) = 0 has equal roots.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.
- [1] 2x²−3x−9 > 0 (For solving quadratic. Ignore > or ≥)
- [1] Critical values x=3 or x=−1½ (condone > or <)
- [1] Set of values: x > 3, or x < −1½
- [3] 2x² − 3x = 2(x−3/4)² − 9/8
- [1] Vertex (3/4, −9/8)
- [1] gf(x) = 3(2x² − 3x) + k = 6x² − 9x + k = 0
- [1] Use of b²−4ac = 0 on 6x² − 9x + k = 0
- [1] k = 27/8 oe.
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