Write the quadratic function in the form $g(x)= a(x-h)^2 + k$ Write the quadratic function in the form $g(x)= a(x-h)^2 + k$ 
Then, give the vertex of its graph.
$g(x)= 2x^2-16x+35$
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I tried, but still lost:
$(2x^2-16x)+35$
$2(x^2-4^2-16)+35$
$2(x^2-4^2-32+35$

I'm not too sure what you did, one of your brackets is missing, but I believe that your error lies in $2(x^2-4^2-16)+35$.
When you complete the square for $x^2+bx$, you take half of $b$ and then square that. However, starting with $x^2+16x$, you subtracted $16$, and then "turned" the $8x$ into a $4^2$. Not possible!
Instead, we're supposed to have$$\begin{align*}2x^2-16x+35 & =2(x^2-8x)+35\\ & =2\left\{x^2-8x+\left(\dfrac {8}2\right)^2-\left(\dfrac 82\right)^2\right\}+35\\ & =2\left(x^2-8x+16\right)+35-32\\ & =2(x-4)^2+3\end{align*}$$
Thus, the vertex of $g(x)$ is $(4,3)$.
