| Date | May 2008 | Marks available | 4 | Reference code | 08M.1.sl.TZ2.2 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 2 | Adapted from | N/A |
Question
The following diagram shows part of the graph of f , where \(f(x) = {x^2} - x - 2\) .
Find both x-intercepts.
[4]
a.
Find the x-coordinate of the vertex.
[2]
b.
Markscheme
evidence of attempting to solve \(f(x) = 0\) (M1)
evidence of correct working A1
e.g. \((x + 1)(x - 2)\) , \(\frac{{1 \pm \sqrt 9 }}{2}\)
intercepts are \(( - 1{\text{, }}0)\) and \((2{\text{, }}0)\) (accept \(x = - 1\) , \(x = 2\) ) A1A1 N1N1
[4 marks]
a.
evidence of appropriate method (M1)
e.g. \({x_v} = \frac{{{x_1} + {x_2}}}{2}\) , \({x_v} = - \frac{b}{{2a}}\) , reference to symmetry
\({x_v} = 0.5\) A1 N2
[2 marks]
b.
Examiners report
This question was consistently the best handled one on the entire paper.
a.
This question was consistently the best handled one on the entire paper.
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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