Answer: First option.
Step-by-step explanation:
By definition, the Vertex form of a Quadratic function is the following:
[tex]f (x) = a(x - h)^2 + k[/tex]
Where [tex](h, k)[/tex] is the vertex of the parabola (Remember that the horizontal shift from [tex]x=0[/tex] is represented by "h" and the vertical shift from [tex]y=0[/tex] is represented by "k").
Now, you can observe in the graph that the vertex ot the given parabola is the following:
[tex](h,k)=(4,-4)[/tex]
So, knowing the vertex, you can identify that the value of "h" and "k" are:
[tex]h=4\\\\y=-4[/tex]
Therefore, with that data you can determine that the equation of the given graph in Vertex form is:
[tex]y= (x - 4)^2 + (-4)\\\\y= (x - 4)^2 -4[/tex]
This matches wih the first option.
