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. **Formula and explanation:** The function is a quadratic polynomial. To find the values at specific points, substitute the $x$ values into the function. 3. **Calculate at $x=1$:** $$y = 1^2 + 2(1) + 1 = 1 + 2 + 1 = 4$$ 4. **Calculate at $x=2$:** $$y = 2^2 + 2(2) + 1 = 4 + 4 + 1 = 9$$ 5. **Interpretation:** At $x=1$, $y=4$ and at $x=2$, $y=9$. This shows the function's value increases as $x$ increases from 1 to 2.