1.39: Quadratic graphs

4PM1/1/January/2018 — Question 1 · 8 marks

f(x)=6+5x-2x^2

Given that

f(x)

can be written in the form

p(x+q)^2+r

, where

p

,

q

and

r

are rational numbers,

(a) find the value of

p

, the value of

q

and the value of

r

. (3)

(b) Hence, or otherwise, find

(i) the maximum value of

f(x)

,

(ii) the value of

x

for which this maximum occurs. (2)

g(x)=6+5x^3-2x^6

(c) Write down

(i) the maximum value of

g(x)

,

(ii) the exact value of

x

for which this maximum occurs. (3)