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).
