Answer
$$4\left(s+\frac{1}{8}\right)^2+\frac{31}{16}$$
Work Step by Step
Completing the square, we find:
$$ 4\left(s^2+\frac{s}{4}+\frac{1}{2}\right) \\ 4\left(\left(s+\frac{1}{8}\right)^2+\frac{1}{2}-\left(\frac{1}{8}\right)^2\right) \\ 4\left(s+\frac{1}{8}\right)^2+\frac{31}{16}$$
