$[$Maximum mark: $4][$without GDC$]$

The graph of the quadratic function below has a vertex at $x=3.$

$($a$)$ Write down the value of $f^{\text{'}}(3).$

$($b$)$ Given that $f(2)=5,$ write down the value of $f(4).$

$($c$)$ Given that $f^{\text{'}}(2)=2,$ write down the value of $f^{\text{'}}(4).$