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Date November 2016 Marks available 2 Reference code 16N.1.SL.TZ0.T_9
Level Standard Level Paper Paper 1 (with calculator from previous syllabus) Time zone Time zone 0
Command term Find Question number T_9 Adapted from N/A

Question

The graph of the quadratic function f(x)=c+bxx2 intersects the x-axis at the point A(1, 0) and has its vertex at the point B(3, 16).

N16/5/MATSD/SP1/ENG/TZ0/09

Write down the equation of the axis of symmetry for this graph.

[2]
a.

Find the value of b.

[2]
b.

Write down the range of f(x).

[2]
c.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

x=3    (A1)(A1)     (C2)

 

Note:     Award (A1) for x= constant, (A1) for the constant being 3.

The answer must be an equation.

 

[2 marks]

a.

b2(1)=3    (M1)

 

Note:     Award (M1) for correct substitution into axis of symmetry formula.

 

OR

b2x=0    (M1)

 

Note:     Award (M1) for correctly differentiating and equating to zero.

 

OR

c+b(1)(1)2=0 (or equivalent)

c+b(3)(3)2=16 (or equivalent)     (M1)

 

Note:     Award (M1) for correct substitution of (1, 0) and (3, 16) in the original quadratic function.

 

(b=) 6    (A1)(ft)     (C2)

 

Note:     Follow through from part (a).

 

[2 marks]

b.

(, 16] OR ], 16]     (A1)(A1)

 

Note:     Award (A1) for two correct interval endpoints, (A1) for left endpoint excluded and right endpoint included.

 

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 2—Functions » SL 2.2—Functions, notation domain, range and inverse as reflection
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