1.18: (a) Express in the form where and are rational numbers to be found.

4PM1/1/November/2023 — Question 2 · 7 marks

g(x)=2x2+12x−3g(x) = 2x^2 + \frac{1}{2}x - 3
(a) Express g(x)\displaystyle g(x) in the form p(x+q)2+r\displaystyle p(x+q)^2 + r where p,q\displaystyle p, q and r\displaystyle r are rational numbers to be found.
(3)
(b) Find
(i) the minimum value of g(x)\displaystyle g(x)
(ii) the value of x\displaystyle x at which this minimum occurs.
(2)
h(x)=2x6+12x3−3h(x) = 2x^6 + \frac{1}{2}x^3 - 3
(c) Hence, or otherwise, write down
(i) the minimum value of h(x)\displaystyle h(x)
(ii) the value of x\displaystyle x at which this minimum occurs.
(2)