19N.1.SL.TZ0.S_3

pestleMathematicsAASLPaper 119N· sl-2-3-graphingsource ↗

Let $g\left( x \right) = {x^2} + bx + 11$ . The point $\left( { - 1{\text{, }}8} \right)$ lies on the graph of $g$ .

Find the value of $b$ .

[3]

The graph of $f\left( x \right) = {x^2}$ is transformed to obtain the graph of $g$ .

Describe this transformation.

[4]

Markscheme / solution

valid attempt to substitute coordinates (M1)

eg $g\left( { - 1} \right) = 8$

correct substitution (A1)

eg ${\left( { - 1} \right)^2} + b\left( { - 1} \right) + 11 = 8$ , $1 - b + 11 = 8$

$b = 4$ A1 N2

[3 marks]

valid attempt to solve (M1)

eg $\left( {{x^2} + 4x + 4} \right) + 7$ , $h = \frac{{ - 4}}{2}$ , $k = g\left( { - 2} \right)$

correct working A1

eg ${\left( {x + 2} \right)^2} + 7$ , $h = - 2$ , $k = 7$

translation or shift (do not accept move) of vector $\left( {\begin{array}{*{20}{c}} { - 2} \\ 7 \end{array}} \right)$ (accept left by $2$ and up by $7$ ) A1A1 N2

[4 marks]

Examiners’ report

[N/A]