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Date May 2008 Marks available 2 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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