Express 2x² + 11x + 6 in the form a(x+b)² + c and find the minimum value.

To do this, take half of the coefficient of $x$ ($\frac{11}{2}$), square it, and add and subtract it within the parenthesis.
Half of $\frac{11}{2}$ is $\frac{11}{4}$.
Squaring $\frac{11}{4}$ gives $(\frac{11}{4})^2 = \frac{121}{16}$.

$$y = 2\left(x^2 + \frac{11}{2}x + \frac{121}{16} - \frac{121}{16}\right) + 6$$

$$y = 2\left(\left(x + \frac{11}{4}\right)^2 - \frac{121}{16}\right) + 6$$ $$y = 2\left(x + \frac{11}{4}\right)^2 - 2\left(\frac{121}{16}\right) + 6$$ $$y = 2\left(x + \frac{11}{4}\right)^2 - \frac{121}{8} + 6$$

$$y = 2\left(x + \frac{11}{4}\right)^2 - \frac{121}{8} + \frac{48}{8}$$ $$y = 2\left(x + \frac{11}{4}\right)^2 - \frac{73}{8}$$

This is in the form $a(x+b)^2 + c$, where $a=2$, $b=\frac{11}{4}$, and $c=-\frac{73}{8}$.

Since $a=2$ is positive, the parabola opens upwards, and the vertex represents the minimum point. The minimum value of the expression $a(x+b)^2 + c$ occurs when $(x+b)^2 = 0$, which means $x = -b$. At this point, the value of $y$ is $c$.
The minimum value is $-\frac{73}{8}$.

The expression in the form $a(x+b)^2 + c$ is:

$$\boxed{y = 2\left(x + \frac{11}{4}\right)^2 - \frac{73}{8}}$$

The minimum value is:

$$\boxed{-\frac{73}{8}}$$