Answer:
Option 4.
Step-by-step explanation:
The vertex form of a parabola is
... (1)
where, a is a constant (h,k) is vertex.
The given function is
![f(x)=x^2](https://tex.z-dn.net/?f=f%28x%29%3Dx%5E2)
The vertex of the function is (0,0) and it goes through (-2, 4) and (2, 4).
It is given that the vertex of function g(x) is at (5,2).
Substitute h=5 and k=2 in equation.
![g(x)=a(x-5)^2+2](https://tex.z-dn.net/?f=g%28x%29%3Da%28x-5%29%5E2%2B2)
g(x) is passes through (3, 6).
.... (2)
![6-2=4a](https://tex.z-dn.net/?f=6-2%3D4a)
![4=4a](https://tex.z-dn.net/?f=4%3D4a)
Divide both sides by 4.
![a=1](https://tex.z-dn.net/?f=a%3D1)
Substitute a=1 in equation (2).
![g(x)=1(x-5)^2+2](https://tex.z-dn.net/?f=g%28x%29%3D1%28x-5%29%5E2%2B2)
![g(x)=(x-5)^2+2](https://tex.z-dn.net/?f=g%28x%29%3D%28x-5%29%5E2%2B2)
The function g(x) is
.
Therefor, the correct option is 4.