1. The problem states that the function $y=2x^2 - 4x + 17$ is horizontally translated two units to the right. 2. Horizontal translation of a function $f(x)$ by $h$ units to the right is given by $f(x-h)$. 3. Here, $h=2$, so the transformed function is $y=2(x-2)^2 - 4(x-2) + 17$. 4. Expand and simplify: $$2(x-2)^2 - 4(x-2) + 17 = 2(x^2 - 4x + 4) - 4x + 8 + 17$$ $$= 2x^2 - 8x + 8 - 4x + 8 + 17$$ $$= 2x^2 - 12x + 33$$ 5. Therefore, the equation for the transformed function is $y = 2x^2 - 12x + 33$. This shows how horizontal shifts affect the function by replacing $x$ with $x-h$ and then simplifying.