1.30: Completing the Square and Minimum Value

4PM1/1/June/2019 — Question 5 · 5 marks

The function f\displaystyle f is defined by
f(x)=3x2−9x+5.f(x)=3x^2-9x+5.
Given that
f(x)=a(x−b)2+c,f(x)=a(x-b)^2+c,
where a\displaystyle a, b\displaystyle b and c\displaystyle c are constants,
(a) find the value of a\displaystyle a, the value of b\displaystyle b and the value of c\displaystyle c.
(3)
(b) Hence write down
(i) the minimum value of f(x)\displaystyle f(x),
(ii) the value of x\displaystyle x for which the minimum value occurs.
(2)