1.28: Past-paper question 2

Given that $\displaystyle f(x)$ can be written in the form $\displaystyle f(x) = a(x+b)^2 + c$ where $\displaystyle a$, $\displaystyle b$ and $\displaystyle c$ are rational numbers,

(a) find the value of $\displaystyle a$, the value of $\displaystyle b$ and the value of $\displaystyle c$

(b) Hence, or otherwise, write down

(i) the minimum value of $\displaystyle f(x)$

(ii) the value of $\displaystyle x$ at which this minimum value occurs.