Higher November 2022 Paper 5 Q18
18
(a) By factorising, find the roots of \(y = x^2 + 18x + 77\). [3]
(b)
(i) Write \(y = x^2 + 18x + 77\) in the form \(y = (x + a)^2 - b\). [3]
(ii) Write down the coordinates of the turning point of the graph of \(y = x^2 + 18x + 77\). [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| \((x + 11)(x + 7)\) [ = 0] | M2 | M1 for \((x + a)(x + b)\) [= 0] where \(ab\) = 77 or \(a + b\) = 18 or for \(x(x + 11) + 7(x + 11)\) or \(x(x + 7) + 11(x + 7)\) | Condone omission of final bracket If partial factors and answers –11 and –7 award M2B1 |
| –11 and –7 | B1 | FT their factors if of the form \((x + a)(x + b)\) with \(a\), \(b\) integers | |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (b)(i) | |||
| \((x + 9)^2 - 4\) final answer | 3 | B1 for \((x + 9)^2\) B2FT for [+] 77 – (their \(a\))2 after (\(x\) + their \(a\))2 correctly evaluated or B1 for [+] 77 – (their \(a\))2 shown If 0 scored, SC2 for final answer \((x + 9) - 4\) | FT can be implied e.g. \((x + 10)^2 - 23\) gets B2FT |
| (b)(ii) | |||
| (–9 , –4) | 2 | FT their 18(b)(i) if in form \((x + a)^2 + b\) B1FT for each value | |