Using the quadratic equation instead of calculus, you can find the x coordinate of the vertex as it will be the midpoint of the two x coordinates of the zeros...
x=(-3±√-27)/2
x=-1.5±√-6.75
That the second term is imaginary does not matter because we will add or subtract this value from -1.5, thus the midpoint of the zeros, the x coordinate of the vertex is -1.5. And to find the value of y for the vertex we just find the value of y when x=-1.5
