y-k=a(x-h)2 is the general form of a parabola with vertex at (h,k).
y-k=a(x2-2xh+h2), y=ax2-2axh+ah2+k.
(h,k)=(-4,12), so y=ax2+8ax+16a+12. Since the y-intercept is 36:
16a+12=36, a=24/16=3/2.
y=3x2/2+12x+36.
y-12=(3/2)(x+4)2. When y=0, -12=(3/2)(x+4)2, (x+4)2=-8, so there are no x intercepts, because all squares are positive. The graph below shows the parabola with vertex (-4,12) and y intercept (0,36). The curve does not intersect the x-axis, showing that there are no x intercepts (the vertex is above the x-axis).