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

Y = a(x  + 1.5)^2 - 12.5
y intercept is (0,-8) so:-
-8 = a(0+1.5)^2 - 12.5
-8 = 2.25a - 12.5
a =  4.5/ 2.25 = 2

so we have 

y  = 2 ( x +1.5)^2 - 12.5

solving for x  when y = 0:-
(x + 1.5)^2 = 12.5/2 = 6.25

taking sqrt's  x + 1.5  = +/- 2.5

x =  -4,   1

so the x intercepts are (-4,0) and (1,0)