| Date | May 2014 | Marks available | 3 | Reference code | 14M.1.sl.TZ1.1 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
Let \(f(x) = a{(x - h)^2} + k\). The vertex of the graph of \(f\) is at \((2, 3)\) and the graph passes through \((1, 7)\).
Write down the value of \(h\) and of \(k\).
[2]
a.
Find the value of \(a\).
[3]
b.
Markscheme
\(h = 2,{\text{ }}k = 3\) A1A1 N2
[2 marks]
a.
attempt to substitute \((1,7)\) in any order into their \(f(x)\) (M1)
eg \(7 = a{(1 - 2)^2} + 3{\text{, }}7 = a{(1 - 3)^2} + 2{\text{, }}1 = a{(7 - 2)^2} + 3\)
correct equation (A1)
eg \(7 = a + 3\)
a = 4 A1 N2
[3 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
Syllabus sections
Topic 2 - Functions and equations » 2.4 » The quadratic function \(x \mapsto a{x^2} + bx + c\) : its graph, \(y\)-intercept \((0, c)\). Axis of symmetry.
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