3.101: Completing the square, sketch and inequality

0606/23/O/N/25 — Question 3 · 9 marks

(a)(i)

Write

x^{2} - 6x - 2

in the form

(x + a)^{2} + b

, where

a

and

b

are constants.

[2]

(a)(ii)

Hence write down the coordinates of the stationary point on

y = x^{2} - 6x - 2

[2]

(b)

On the axes, draw the graph of

y = x^{2} - 6x - 2

for

-4 \leqslant x \leqslant 4

[3]

(c)

Use your graph to solve the inequality

x^{2} - 6x - 2 \leqslant 4

[2]