The x-location of the vertex of ax²+bx+c is x=-b/(2a). For your parabola, that is
x = -6/(2·3) = -1
The vertex y-value is then
f(-1) = 3 -6 -24 = -27
When you move 1 unit either side of the vertex, the value of f(x) changes by the coefficient of x², which is +3. Now, you know
vertex = (-1, -27)
another point = (0, -24)
