| Date | November 2017 | Marks available | 3 | Reference code | 17N.1.sl.TZ0.11 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 11 | Adapted from | N/A |
Question
A quadratic function \(f\) is given by \(f(x) = a{x^2} + bx + c\). The points \((0,{\text{ }}5)\) and \(( - 4,{\text{ }}5)\) lie on the graph of \(y = f(x)\).
The \(y\)-coordinate of the minimum of the graph is 3.
Find the equation of the axis of symmetry of the graph of \(y = f(x)\).
Write down the value of \(c\).
Find the value of \(a\) and of \(b\).
Markscheme
\(x = - 2\) (A1)(A1) (C2)
Note: Award (A1) for \(x = \) (a constant) and (A1) for \( - 2\).
[2 marks]
\((c = ){\text{ }}5\) (A1) (C1)
[1 mark]
\( - \frac{b}{{2a}} = - 2\)
\(a{( - 2)^2} - 2b + 5 = 3\) or equivalent
\(a{( - 4)^2} - 4b + 5 = 5\) or equivalent
\(2a( - 2) + b = 0\) or equivalent (M1)
Note: Award (M1) for two of the above equations.
\(a = 0.5\) (A1)(ft)
\(b = 2\) (A1)(ft) (C3)
Note: Award at most (M1)(A1)(ft)(A0) if the answers are reversed.
Follow through from parts (a) and (b).
[3 marks]
