Answer:
domain F(x) = All real numbers
Range F(x)  [ -2 ,  + ∞ ]
Step-by-step explanation:
There are three points of the curve
P₁ ( -1,5 , 0 )   Q ( 0. -2 ) and P₂ ( 1,5 , 0 )
We can see that P₁   and P₂  are simmetric around y axis, and point Q looks like a vertex we conclude the curve is of the form
ax² + bx + c = y
The curve is a parabola 
when x = 0      y = -2     then   c  = - 2
And  plugging in the coordinates of the points in the equation we get:
a (-1,5)²  +  b (-1,5) + c = 0      ⇒  2,25*a  - 1,5*b - 2 = 0
a (1,5)²   +  b ( 1,5)  + c = 0     ⇒   2,25*a + 1,5*b -2 = 0
Adding these two equations 
4.5*a - 4 = 0
a =  4/4,5
as vertex is  Q ( 0 , -2 )
x = - b/2a      ⇒   0 = - b/ 9      ⇒  b  =  0
Therefore the equation of the function is:
ax² + c = 0
(4/4,5) x² - 2 = 0
Having the equation we can determine Domain
domain F(x) = All real numbers
Range F(x)  [ -2 ,  + ∞ ]