| Date | November 2016 | Marks available | 2 | Reference code | 16N.1.sl.TZ0.1 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 1 | Adapted from | N/A |
Question
Let \(f(x) = {x^2} - 4x + 5\).
The function can also be expressed in the form \(f(x) = {(x - h)^2} + k\).
Find the equation of the axis of symmetry of the graph of \(f\).
(i) Write down the value of \(h\).
(ii) Find the value of \(k\).
Markscheme
correct approach (A1)
eg \(\frac{{ - ( - 4)}}{2},{\text{ }}f'(x) = 2x - 4 = 0,{\text{ (}}{x^2} - 4x + 4) + 5 - 4\)
\(x = 2\) (must be an equation) A1 N2
[2 marks]
(i) \(h = 2\) A1 N1
(ii) METHOD 1
valid attempt to find \(k\) (M1)
eg\(\,\,\,\,\,\)\(f(2)\)
correct substitution into their function (A1)
eg\(\,\,\,\,\,\)\({(2)^2} - 4(2) + 5\)
\(k = 1\) A1 N2
METHOD 2
valid attempt to complete the square (M1)
eg\(\,\,\,\,\,\)\({x^2} - 4x + 4\)
correct working (A1)
eg\(\,\,\,\,\,\)\(({x^2} - 4x + 4) - 4 + 5,{\text{ }}{(x - 2)^2} + 1\)
\(k = 1\) A1 N2
[4 marks]
