16N.1.SL.TZ0.S_1

pestleMathematicsAASLPaper 116N· sl-2-6-quadratic-functionsource ↗

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

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

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

(ii) Find the value of $k$ .

Markscheme / solution

(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]