16N.1.SL.TZ0.S_1

pestleMathematicsAISLPaper 116N· sl-2-5-modelling-functionssource ↗

Let $f(x) = {x^2} - 4x + 5$ .

The function can also be expressed in the form $f(x) = {(x - h)^2} + k$ .

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

[2]

(i) Write down the value of $h$ .

(ii) Find the value of $k$ .

[4]

Markscheme / solution

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

correct approach (A1)

eg $\frac{{ - ( - 4)}}{2},{\text{ }}f'(x) = 2x - 4 = 0,{\text{ (}}{x^2} - 4x + 4) + 5 - 4$

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

[2 marks]

(i) $h = 2$ A1 N1

(ii) METHOD 1

valid attempt to find $k$ (M1)

eg $\,\,\,\,\,$ $f(2)$

correct substitution into their function (A1)

eg $\,\,\,\,\,$ ${(2)^2} - 4(2) + 5$

$k = 1$ A1 N2

METHOD 2

valid attempt to complete the square (M1)

eg $\,\,\,\,\,$ ${x^2} - 4x + 4$

correct working (A1)

eg $\,\,\,\,\,$ $({x^2} - 4x + 4) - 4 + 5,{\text{ }}{(x - 2)^2} + 1$

$k = 1$ A1 N2

[4 marks]

Examiners’ report

[N/A]