Higher June 2022 Paper 6 Q16
16 Frankie sketches this quadratic graph.
Not to scale
Frankie says
The \(y\)-intercept is 15.
(a) Show that what Frankie says could be correct. [3]
(b) Explain why what Frankie says may not be correct. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| E.g. [\(y =\)] \(-(x + 3)(x - 5)\) AND either [\(y = -x^2 - 3x + 5x\)] + 15 or [Constant/\(y\)-intercept =] \(-3 \times -5 = 15\) | 3 | M2 for [\(y =\)] \(-(x + 3)(x - 5)\) or M1 for \(k(x + 3)(x - 5)\) | See Appendix For full marks, all shown parts of their expansion must be correct Accept \(k\) implied as 1 |
| Alternative method using simultaneous equations \(y = -x^2 + bx + c\) \(0 = -(-3)^2 - 3b + c\) and \(0 = -5^2 + 5b + c\) [\(b = 2\)] \(c = 15\) | M2 for \(0 = -(-3)^2 - 3b + c\) and \(0 = -5^2 + 5b + c\) or M1 for \(y = -x^2 + bx + c\) or for \(0 = (-3)^2 - 3b + c\) and \(0 = 5^2 + 5b + c\) | ||
Appendix: exemplar response for Q16(a)
| Response | Judgement | Mark |
|---|---|---|
| \((x + 3)(x - 5)\) \(= x^2 - 2x - 15\) But the quadratic is upside down so it will be \(-x^2 + 2x + 15\) [there then was an arrow from the +15 to the intercept] | The response doesn’t quite fit the scheme but is thought worthy of full marks This line on its own scores M1 But this line makes it equivalent to the M2 and it also a correct expansion with + 15 The linking of +15 to the intercept is an added bonus |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| The equation could be a multiple E.g. [\(y =\)] \(-k(x + 3)(x - 5)\) So the intercept could be a multiple of 15 | 2 | B1 for giving an example in the form \(-k(x + 3)(x - 5)\) (where \(k > 0\), \(k \ne 1\), \(k\) need not be an integer) or stating that the intercept could be a multiple of 15 | Allow full or part marks for a fully correct algebraic example E.g. [\(y =\)] \(-2(x + 3)(x - 5)\) would have a \(y\)-intercept of 30 |