3.17: Completing the square and inverse function domain

0606/12/O/N/25 — Question 4 · 10 marks

(a)

Show that

x^{2} + 2x + 5

can be written as

(x + a)^{2} + b

, where

a

and

b

are constants.

[2]

(b)

Hence write down the coordinates of the stationary point on

y = x^{2} + 2x + 5

[2]

(c)(i)

A function

f

is such that

f(x) = x^{2} + 2x + 5

for

x \geqslant p

. Given that

f^{-1}

exists, write down the least possible value of

p

[1]

(c)(ii)

Using your value of

p

, sketch

y = f(x)

and

y = f^{-1}(x)

. Label each graph and state the intercepts with the axes.

[5]