Respuesta :

kudzordzifrancis
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.

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