ANSWER
[tex]f(x) = (x + 3)^{2} - 1[/tex]
EXPLANATION
The vertex of the graph is at
[tex](-3,-1)[/tex]
The equation of the graph in vertex form is given by the formula,
[tex]f(x) = a{(x - h)}^{2} + k[/tex]
The above graph has a minimum point, hence
[tex]a > \: 0[/tex]
When we put these values into the equation we obtain,
[tex]f(x) = a(x - - 3)^{2} + - 1[/tex]
This implies that,
[tex]f(x) = a(x + 3)^{2} - 1[/tex]
The point (-2,0) lies on the line.
[tex]a( - 2 + 3)^{2} - 1 = 0[/tex]
[tex]a = 1[/tex]
[tex]f(x) = (x + 3)^{2} - 1[/tex]
The correct answer is D.
