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Date May 2017 Marks available 4 Reference code 17M.1.SL.TZ1.T_15
Level Standard Level Paper Paper 1 Time zone Time zone 1
Command term Find Question number T_15 Adapted from N/A

Question

The graph of a quadratic function has y -intercept 10 and one of its x -intercepts is 1.

The x -coordinate of the vertex of the graph is 3.

The equation of the quadratic function is in the form y = a x 2 + b x + c .

Write down the value of c .

[1]
a.

Find the value of a and of b .

[4]
b.

Write down the second x -intercept of the function.

[1]
c.

Markscheme

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

10     (A1)     (C1)

 

Note:     Accept ( 0 ,   10 ) .

 

[1 mark]

a.

3 = b 2 a

0 = a ( 1 ) 2 + b ( 1 ) + c

10 = a ( 6 ) 2 + b ( 6 ) + c

0 = a ( 5 ) 2 + b ( 5 ) + c     (M1)(M1)

 

Note:     Award (M1) for each of the above equations, provided they are not equivalent, up to a maximum of (M1)(M1). Accept equations that substitute their 10 for c .

 

OR

sketch graph showing given information: intercepts ( 1 ,   0 ) and ( 0 ,   10 ) and line x = 3     (M1)

y = a ( x 1 ) ( x 5 )     (M1)

 

Note:     Award (M1) for ( x 1 ) ( x 5 ) seen.

 

a = 2     (A1)(ft)

b = 12     (A1)(ft)     (C4)

 

Note:     Follow through from part (a).

If it is not clear which is a and which is b award at most (A0)(A1)(ft).

 

[4 marks]

b.

5     (A1)     (C1)

[1 mark]

c.

Examiners report

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

Syllabus sections

Topic 2—Functions » SL 2.4—Key features of graphs, intersections using technology
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