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Date	May 2016	Marks available	2	Reference code	16M.1.sl.TZ2.1
Level	SL only	Paper	1	Time zone	TZ2
Command term	Write down	Question number	1	Adapted from	N/A

Question

The following diagram shows part of the graph of a quadratic function $f$ .

M16/5/MATME/SP1/ENG/TZ2/01

The vertex is at $(3,{\text{ }} - 1)$ and the $x$ -intercepts at 2 and 4.

The function $f$ can be written in the form $f(x) = {(x - h)^2} + k$ .

The function can also be written in the form $f(x) = (x - a)(x - b)$ .

Write down the value of $h$ and of $k$ .

[2]

Write down the value of $a$ and of $b$ .

[2]

Find the $y$ -intercept.

[2]

Markscheme

$h = 3,{\text{ }}k = - 1$ A1A1 N2

[2 marks]

$a = 2,{\text{ }}b = 4{\text{ }}({\text{or }}a = 4,{\text{ }}b = 2)$ A1A1 N2

[2 marks]

attempt to substitute $x = 0$ into their $f$ (M1)

eg $\,\,\,\,\,$ ${(0 - 3)^2} - 1,{\text{ }}(0 - 2)(0 - 4)$

$y = 8$ A1 N2

[2 marks]

Examiners report

Nearly all candidates performed well on this question, earning full marks on all three question parts.

Nearly all candidates performed well on this question, earning full marks on all three question parts. In part (b), there were some candidates who factored the quadratic expression correctly, but went on to give negative values for $a$ and $b$ .

Nearly all candidates performed well on this question, earning full marks on all three question parts.

Syllabus sections

Topic 2 - Functions and equations » 2.2 » Investigation of key features of graphs, such as maximum and minimum values, intercepts, horizontal and vertical asymptotes, symmetry, and consideration of domain and range.

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