1. The problem is to verify if the point $(2,9)$ lies on the curve defined by the function $y = 3x^2 - 2x + 1$. 2. Substitute $x = 2$ into the function: $$y = 3(2)^2 - 2(2) + 1$$ 3. Calculate step-by-step: $$y = 3 \times 4 - 4 + 1 = 12 - 4 + 1 = 9$$ 4. The calculated $y$ value is $9$, which matches the $y$ coordinate of the point given. 5. Therefore, the point $(2,9)$ lies on the curve $y = 3x^2 - 2x + 1$.