Answer
$ f(x) = (x-3.5)^2-2.25 $
Work Step by Step
The conversion of the function to the standard vertex form $f(x)=a(x-h)^2+k$ is self explanatory. All mathematical steps are shown below.$$
\begin{aligned}
f(x)&=x^2-7 x+10\\
& = x^2-7 x+\left(\frac{7}{2}\right)^2 +10-\left(\frac{7}{2}\right)^2 \\
& =\left(x^2-7 x+3.5^2\right)+10-3.5^2 \\
& =(x-3.5)^2-2.25.
\end{aligned}
$$ The vertex form of the given function is $$f(x)=(x-3.5)^2-2.25.$$
