Answer
$f(x)=3x^{2}-x-3$
Work Step by Step
A function with $f^{\prime}(x)=6x-1$ (for all x)
has form $f(x)=3x^{2}-x+c$,
where c is some constant.
The point $(2,7)$ is on the graph, so
$f(2)=7$
Since $f(2)=3(2^{2})-2+c$,
$7=10+c$,
it follows that $c=-3$ and
$f(x)=3x^{2}-x-3$
