we know that
The graph represent a vertical parabola
The equation of a vertical parabola open upward in vertex form is equal to
y=a(x-h)^2+k
where
a is the leading coefficient
(h,k) is the vertex
In this problem we have
the vertex is (-3,-2) -----> see the graph
substitute
y=a(x+3)-2
Find the value of a
we have that
For x=-2, the valuue of y=0
substitute
0=a(-2+3)^2-2
0=a-2
a=2
therefore
the equation is
y=2(x+3)-2
REwrite
y+2=2(x+3)^2