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).
