How do you write the vertex form equation of the parabola #y=2x^2 +11x-6#?

The easist way to find the vertex is to complete the square:

y=2x^2 +11x-6  =>  y=2[ x^2 + (11/2)x  + (11/2)^2   - (11/2)^2 ]  - 6  

This can be rewritten as 
                                y = 2[(x+11/2)^2 ] -(121/4) - 24/4

                                y = 2 (x+11/2)^2 - 145/4

this is the equation in vertex form.  The vertex is at (-11/2, -145/4).