17N.1.SL.TZ0.T_11

pestleMathematicsAISLPaper 117N· sl-2-5-modelling-functionssource ↗

A quadratic function $f$ is given by $f(x) = a{x^2} + bx + c$ . The points $(0,{\text{ }}5)$ and $( - 4,{\text{ }}5)$ lie on the graph of $y = f(x)$ .

The $y$ -coordinate of the minimum of the graph is 3.

Find the value of $a$ and of $b$ .

Markscheme / solution

$- \frac{b}{{2a}} = - 2$

$a{( - 2)^2} - 2b + 5 = 3$ or equivalent

$a{( - 4)^2} - 4b + 5 = 5$ or equivalent

$2a( - 2) + b = 0$ or equivalent (M1)

Note: Award (M1) for two of the above equations.

$a = 0.5$ (A1)(ft)

$b = 2$ (A1)(ft) (C3)

Note: Award at most (M1)(A1)(ft)(A0) if the answers are reversed.

Follow through from parts (a) and (b).

[3 marks]

Examiners’ report

[N/A]