<s>[INST] 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:
$(2x^2-16x)+35$
$2(x^2-4^2-16)+35$
$2(x^2-4^2-32+35$
 [/INST] It may be prudent to write out all of the steps without any shortcuts.
$$\begin{align}
g(x)&=2x^2 - 16x + 35\\
g(x)&=2(x^2 - 8x) + 35\\
g(x)&=2(x^2 - 8x) + 35\\
g(x)&=2(x^2 - 4x -4x) + 35\\
g(x)&=2(x^2 - 4x -4x + 0) + 35\\
g(x)&=2(x^2 - 4x -4x + 16 - 16) + 35\\
g(x)&=2(x^2 - 4x -4x + 16) -32 + 35\\
g(x)&=2(x(x - 4) -4(x - 4)) +3\\
g(x)&=2(x - 4)(x - 4) +3\\
g(x)&=2(x - 4)^2 +3\\
\end{align}$$
You know that the vertex will occur when $x-h = 0$. Maybe draw a table of values, or draw a graph, or both to determine the coordinates of the vertex.
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