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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=ax2+bx+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=b2a

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(x1)(x5)     (M1)

 

Note:     Award (M1) for (x1)(x5) 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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