16N.1.SL.TZ0.T_9

pestleMathematicsAISLPaper 116N· sl-2-2-functions-notation-domain-range-and-inverse-as-reflectionsource ↗

The graph of the quadratic function $f(x) = c + bx - {x^2}$ intersects the $x$ -axis at the point ${\text{A}}( - 1,{\text{ }}0)$ and has its vertex at the point ${\text{B}}(3,{\text{ }}16)$ .

N16/5/MATSD/SP1/ENG/TZ0/09

Find the value of $b$ .

Markscheme / solution

$\frac{{ - b}}{{2( - 1)}} = 3$ (M1)

Note: Award (M1) for correct substitution into axis of symmetry formula.

$b - 2x = 0$ (M1)

Note: Award (M1) for correctly differentiating and equating to zero.

$c + b( - 1) - {( - 1)^2} = 0$ (or equivalent)

$c + b(3) - {(3)^2} = 16$ (or equivalent) (M1)

Note: Award (M1) for correct substitution of $( - 1,{\text{ }}0)$ and $(3,{\text{ }}16)$ in the original quadratic function.

$(b = ){\text{ }}6$ (A1)(ft) (C2)

Note: Follow through from part (a).

[2 marks]

Examiners’ report

[N/A]