1. **State the problem:** We need to find the values of the function $y = x^2 + 2x + 1$ for $x$ from 1 to 2. 2. **Recall the function:** The function is a quadratic polynomial given by $$y = x^2 + 2x + 1$$ 3. **Evaluate at $x=1$:** $$y(1) = 1^2 + 2(1) + 1 = 1 + 2 + 1 = 4$$ 4. **Evaluate at $x=2$:** $$y(2) = 2^2 + 2(2) + 1 = 4 + 4 + 1 = 9$$ 5. **Interpretation:** The function value increases from 4 at $x=1$ to 9 at $x=2$. **Final answer:** $$y(1) = 4, \quad y(2) = 9$$