The vertex of a parabola is (-1.5, -12.5), and its y-intercept is (0, -8) the x-intercepts of the parabola are: (-2, 0), (-4, 0), (2, 0), (4, 0) and (-1, 0), (2, 0), (1, 0), (-2, 0)

Best to find the equation of the parabola first:

Its equation is y+12.5 = (x+1.5)^2, or y = -12.5 + (x+1.5)^2

Check the first possible x-intercept:  let x = -2.  Does y come out to 0?

y = -12.5 + (-0.5)^2  =  -12.5 + 0.25.  This is not equal to 0, so (-2,0) is not an x-intercept of this parabola.  Continue checking each possible x-intercept until you find the right one (or ones).