20N.1.SL.TZ0.T_11

pestleMathematicsAASLPaper 120N· sl-2-6-quadratic-functionsource ↗

The diagram shows the graph of the quadratic function $f (x) = a x^{2} + b x + c$ , with vertex $(- 2, 10)$ .

The equation $f (x) = k$ has two solutions. One of these solutions is $x = 2$ .

Write down the other solution of $f (x) = k$ .

[2]

Complete the table below placing a tick (✔) to show whether the unknown parameters $a$ and $b$ are positive, zero or negative. The row for $c$ has been completed as an example.

[2]

State the values of $x$ for which $f (x)$ is decreasing.

[2]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure. It appeared in a paper that permitted the use of a calculator, and so might not be suitable for all forms of practice.

$(x =) (- 2) - 4$ OR $(x =) (- 2) - (2 - (- 2))$ (M1)

Note: Award (M1) for correct calculation of the left symmetrical point.

$(x =) - 6$ (A1) (C2)

[2 marks]

(A1)(A1) (C2)

Note: Award (A1) for each correct row.

[2 marks]

$x > - 2$ OR $x \geq - 2$ (A1)(A1) (C2)

Note: Award (A1) for $- 2$ seen as part of an inequality, (A1) for completely correct notation. Award (A1)(A1) for correct equivalent statement in words, for example “decreasing when $x$ is greater than negative $2$ ”.

[2 marks]

Examiners’ report

[N/A]