There are two possibilities for the equation.
One is: y = 2x^2 + 4sqrt(3)x + 6
The other is: y = 2x^2 - 4sqrt(3)x + 6.
Both of these curves look very different, but both of them will touch the x axis once (NB Quadratic equations can't intersect the x axis only once, it can only just touch it in one place).