The standard form of the equation of a parabola is y = 2x2 + 16x + 17. what is the vertex form of the equation?

The vertex form looks like y-k = a(x-h)^2.  We must re-write y = 2x^2 + 16x + 17 in this vertex form.

Note that y = 2x^2 + 16 x + 17 can be re-written as y = 2(x^2 + 8x) + 17

Let's complete the square:  to x^2 + 8x add 4^2, and then subtract 4^2:

y = 2(x^2 + 8x + 16 - 16) + 17.  This become y = 2(x^2 + 8x + 16) + 1, or

y = 2(x+4)^2 + 1   (answer),    or y - 1 = 2(x-[-4])^2 + 1.  The vertex is
at (-4, 1).