Answer : The correct option is, (A) [tex]g(x)=(x-4)^{2}[/tex]
Step-by-step explanation :
As we given that:
[tex]f(x)=x^{2}[/tex]
The point of vertex of f(x) is (0, 0)
The point of vertex of g(x) is (4, 0) [from the graph]
The rule of the translation is:
f(x) → g(x)
(x, y) → (x+4, y+0)
The equation of the function g(x) in the vertex form is:
[tex]g(x)=(x-h)^{2}+k[/tex]
where,
(h, k) is the vertex
(h, k) = (4, 0)
Now put the vale of h and k, we get:
[tex]g(x)=(x-4)^{2}+0[/tex]
[tex]g(x)=(x-4)^{2}[/tex]
Therefore, the equation of the blue graph is, [tex]g(x)=(x-4)^{2}[/tex]
