Answer:
Option D.
Step-by-step explanation:
From the given graph it is clear that it is a parabola along to the x-axis.
Vertex form of a parabola along the x-axis is
[tex]x=a(y-k)^2+h[/tex]
where, (h,k) is vertex.
From the graph it is clear that the vertex of the parabola is (4,-3). So, substitute h=4 and k=-3 in the above equation.
[tex]x=a(y-(-3))^2+(4)[/tex]
[tex]x=a(y+3)^2+4[/tex] ...(1)
The graph passing through (1,-2), so substitute x=1 and y=-2 in the above equation.
[tex]1=a(-2+3)^2+4[/tex]
[tex]1-4=a(1)^2[/tex]
[tex]-3=a(1)^2[/tex]
Substitute a=-3 in equation (1).
[tex]x=-3(y+3)^2+4[/tex]
Therefore, the correct option is D.
