| Date | November 2009 | Marks available | 2 | Reference code | 09N.1.sl.TZ0.13 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Calculate | Question number | 13 | Adapted from | N/A |
Question
The diagram below shows the graph of a quadratic function. The graph passes through the points (6, 0) and (p, 0). The maximum point has coordinates (0.5, 30.25).
Calculate the value of p.
Given that the quadratic function has an equation \(y = -x^2 + bx + c\) where \(b,{\text{ }}c \in \mathbb{Z}\), find \(b\) and \(c\).
Markscheme
\(\frac{{(p + 6)}}{2} = 0.5\) (M1)
\(p = -5\) (A1) (C2)
[2 marks]
\(\frac{{ - b}}{{2( - 1)}} = 0.5\) (M1)
\(b = 1\) (A1)
\(- 0.5^2 + 0.5 + c = 30.25\) (M1)
\(c = 30\) (A1)(ft)
Note: Follow through from their value of b.
OR
\(y = (6 - x) (5 + x)\) (M1)
\(= 30 + x - x^2\) (A1)
\(b = 1,{\text{ }}c = 30\) (A1)(A1)(ft) (C4)
Note: Follow through from their value of p in part (a).
[4 marks]
Examiners report
This question was one of the most difficult in this paper. Many students left this question blank, showed incorrect working or gave answers without any preceding working.
This question was one of the most difficult in this paper. Many students left this question blank, showed incorrect working or gave answers without any preceding working.
