QPaperGen

We have:
\[
(2x - 1)^2 \geq 0 \text{ for all } x \in \mathbb{R}
\]
\[
f(x) = (2x - 1)^2 + 3 \geq 3 \text{ for all } x \in \mathbb{R}
\]
Minimum value occurs when \(2x - 1 = 0 \Rightarrow x = \frac{1}{2}\).
\[
\text{Minimum value of } f\left(\frac{1}{2}\right) = (2 \cdot \frac{1}{2} - 1)^2 + 3 = 3
\]
No maximum value exists since the function is unbounded above.