First the x - intercepts are given by the solutions to the follwoing equation:
x^2-x-6 = 0
The solutions are x = 3, x = -2, which reresent the x intercepts namely the set of points: (3, 0), (-2, 0).
The y intercepts are found by substituting 0 in every x:
0 - 0 - 6 = 0 => (0, -6) - the y intercept.
The vertex is given by the formula V(-b/2a, -delta/4) =>
V(1/2, -25/4).