3.29: Completing the square, stationary point and sketch

0606/11/M/J/23 — Question 1 · 10 marks

(a)

Write

5x^{2} - 14x + 8

in the form

a(x + b)^{2} + c

, where

a

b

and

c

are constants.

[3]

(b)

Hence write down the coordinates of the stationary point on

y = 5x^{2} - 14x + 8

[2]

(c)

Sketch the graph of

y = 5x^{2} - 14x + 8

, stating the coordinates where it meets the axes.

[3]

(d)

Write down the range of values of

k

for which

\left\lvert 5x^{2} - 14x + 8\right\rvert = k

has

4

distinct roots.

[2]