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Date May 2014 Marks available 2 Reference code 14M.1.sl.TZ1.13
Level SL only Paper 1 Time zone TZ1
Command term Find Question number 13 Adapted from N/A

Question

The graph of the quadratic function \(f(x) = a{x^2} + bx + c\) intersects the y-axis at point A (0, 5) and has its vertex at point B (4, 13).


Write down the value of \(c\).

[1]
a.

By using the coordinates of the vertex, B, or otherwise, write down two equations in \(a\) and \(b\).

[3]
b.

Find the value of \(a\) and of \(b\).

[2]
c.

Markscheme

5     (A1)     (C1)

[1 mark]

a.

at least one of the following equations required

\(a{(4)^2} + 4b + 5 = 13\)

\(4 =  - \frac{b}{{2a}}\)

\(a{(8)^2} + 8b + 5 = 5\)     (A2)(A1)     (C3)

 

Note: Award (A2)(A0) for one correct equation, or its equivalent, and (C3) for any two correct equations.

     Follow through from part (a).

     The equation \(a{(0)^2} + b(0) = 5\) earns no marks.

 

[3 marks]

b.

\(a =  - \frac{1}{2},{\text{ }}b = 4\)     (A1)(ft)(A1)(ft)     (C2)

 

Note: Follow through from their equations in part (b), but only if their equations lead to unique solutions for \(a\) and \(b\).

 

[2 marks]

c.

Examiners report

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

Syllabus sections

Topic 1 - Number and algebra » 1.6 » Use of a GDC to solve pairs of linear equations in two variables.

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