A-LevelMathematicsQuadratics9709/12 · May/June 2020 · Q66 Marks
The equation of a curve is y = 2x² + kx + k − 1, where k is a constant.
- (a)Given that the line y = 2x + 3 is a tangent to the curve, find the value of k.[3]
- (b)It is now given that k = 2. Express the equation of the curve in the form y = 2(x + a)² + b, where a and b are constants, and hence state the coordinates of the vertex of the curve.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [M1] 2x² + kx + k - 1 = 2x + 3 → 2x² + (k-2)x + k - 4 = 0
- [M1] Use of b² - 4ac = 0 → (k - 2)² = 8(k - 4)
- [A1] k = 6
- [B1 B1] 2x² + 2x + 1 = 2(x + 1/2)² + 1/2. a = 1/2, b = 1/2
- [B1FT] vertex (-1/2, 1/2) (FT on a and b values)
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