Answer
$f(x) = 0.2\left(x-17.5\right)^2-71.25$
Work Step by Step
The conversion of the function to the standard vertex form is self explanatory. All mathematical steps are shown below. $$
\begin{aligned}
f(x)&=0.2 x^2-7 x-10\\
& = 0.2\left( x^2-\frac{7}{0.2} x\right) -10\\
&= 0.2\left( x^2-35x\right) -10\\
& = 0.2\left[ x^2-35x+\left( \frac{35}{2}\right)^2\right]-10-0.2\cdot \left( \frac{35}{2}\right)^2\\
& = 0.2\left(x^2-35x+ 17.5^2 \right)-10-0.2\cdot 17.5^2 \\
& =0.2\left(x-17.5\right)^2-71.25\\
\end{aligned}
$$
