Answer:
(4, 2)
Explanation:
y = 2x^2 - 16x +34 can be simplified by factoring out 2 from all three terms on the right side: y = 2(x^2 - 8x + 17).
We need to "complete the square" here. Notice that the coefficient of x is -8; we take half of that (which is -4) and square this result (which yields 16).
Focusing on x^2 - 8x + 17, we add 16, and then subtract 16, obtaining:
x^2 - 8x + 16 - 16 + 17, or (x - 4)^2 + 1
Now return to the original function, y = 2(x^2 - 8x + 17).
Replace x^2 - 8x + 17 with [x - 4]^2 + 1:
We get y = 2(x^2 - 8x + 17). = 2( [x - 4]^2 + 1 )
This has the form y = a(x - h)^2 + k, and by comparison we see that h = 4 and k = 2. The vertex of this parabola is at (4, 2).