The equation of the graph would be a quadratic equation. The vertex form of a quadratice equation is expresses as
y = a(x - h)^2 + k
where
h and k are the x and y coordinates of the vertex(bottom) of the graph. Lookong at the vertex of the graph,
x = - 3 and y = 1
Thus, h = - 3 and k = 1
Substituting h = - 3 and k = 1 into the vertex form equation, it becomes
y = a(x - - 3)^2 + 1
y = a(x + 3)^2 + 1 ---------------------1
We would pick corresponding x and y values from the curve. We have
when x = - 2, y = 3
Substituting x = - 2 and y = 3 into equation 1, we have
3 = a(- 2 + 3)^2 + 1
3 = a(1)^2 + 1
3 = a + 1
a = 3 - 1 = 2
Substituting a = 2 into equation 1, we have
y = 2(x + 3)^2 + 1
The correct option is B