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Date November 2018 Marks available 3 Reference code 18N.1.SL.TZ0.S_8
Level Standard Level Paper Paper 1 Time zone Time zone 0
Command term Find Question number S_8 Adapted from N/A

Question

Let f(x)=x24x5. The following diagram shows part of the graph of f.

The function can be written in the form f(x)=(xh)2+k.

Find the equation of the axis of symmetry of the graph of f.

[2]
b.

Write down the value of h.

[1]
c.i.

Find the value of k.

[3]
c.ii.

The graph of a second function, g, is obtained by a reflection of the graph of f in the y-axis, followed by a translation of (36).

 

Find the coordinates of the vertex of the graph of g.

[5]
d.

Markscheme

correct working      (A1)

eg   (4)2(1),  1+52

 

x=2  (must be an equation with x=)      A1 N2

 

[2 marks]

b.

h = 2      A1  N1

 

[1 mark]

c.i.

METHOD 1

valid approach      (M1)

eg   f(2)

correct substitution      (A1)

eg   (2)2 − 4(2) − 5

k = −9     A1 N2

 

METHOD 2

valid attempt to complete the square      (M1)

eg   x2 − 4x + 4

correct working      (A1)

eg  (x2 − 4x + 4) − 4 − 5,  (x − 2)2 − 9

k = −9     A1 N2

 

[3 marks]

c.ii.

 

METHOD 1 (working with vertex)

vertex of f is at (2, −9)      (A1)

correct horizontal reflection      (A1)

eg  x = −2,  (−2, −9)

valid approach for translation of their x or y value      (M1)

eg   x − 3,  y + 6,  (29)+(36),  one correct coordinate for vertex

vertex of g is (−5, −3) (accept x = −5, y = −3)      A1A1 N1N1

 

METHOD 2 (working with function)

correct approach for horizontal reflection      (A1)

eg   f(−x)

correct horizontal reflection      (A1)

eg   (−x)2 −4(−x) − 5,   x+ 4x − 5, (−x − 2)2 − 9

valid approach for translation of their x or y value      (M1)

eg   (x + 3)2 + 4(x + 3) − 5 + 6,  x2 + 10x + 22,  (x + 5)2 − 3,  one correct coordinate for vertex

vertex of g is (−5, −3) (accept x = −5, y = −3)      A1A1 N1N1

 

[5 marks]

d.

Examiners report

[N/A]
b.
[N/A]
c.i.
[N/A]
c.ii.
[N/A]
d.

Syllabus sections

Topic 2—Functions » SL 2.5—Modelling functions
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Topic 2—Functions » AHL 2.8—Transformations of graphs, composite transformations
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