Application Of Derivatives

the distance between $(-1,2)$ and $(a, f(A)$, where $x=a$ is the point of local minima is $2 \sqrt{5}$

$f(x)$ is increasing for $x \in[1,2 \sqrt{5}]$

$f(x)$ has local minima at $x=1$

the value of $f(0)=5$