Answer:
[tex]f(x)=(x-4)^{2}[/tex]
Step-by-step explanation:
we have that
The axis of symmetry shown in the graph is x=4
we know that
The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex
so
Verify each case
case a) we have
[tex]f(x)=(x+4)^{2}[/tex]
The vertex is the point (-4,0)
therefore
Cannot be the function
case b) we have
[tex]f(x)=x^{2}+4[/tex]
The vertex is the point (0,4)
The axis of symmetry is x=0
therefore
Cannot be the function
case c) we have
[tex]f(x)=(x-4)^{2}[/tex]
The vertex is the point (4,0)
The axis of symmetry is x=4
therefore
Could be the function
case d) we have
[tex]f(x)=x^{2}-4[/tex]
The vertex is the point (0,-4)
The axis of symmetry is x=0
therefore
Cannot be the function
