The graph of the parent function
f(x) = x^2 is reflected across the y-axis. write an
equation for the function g after the reflection.
show your work. based on your equation, what
happens to the graph? explain.

g(x) = x²

The graph of g(x) is the same with the graph of f(x)

Step-by-step explanation:

* Lets explain how to solve the problem

- If the function f(x) reflected across the x-axis, then the new  

 function g(x) = - f(x)

- If the function f(x) reflected across the y-axis, then the new

 function g(x) = f(-x)

* Lets solve the problem

∵ The parent function f(x) = x² is represent by upward parabola

   with vertex (0 , 0) (red graph in the attached picture)

∵ f(x) is reflected across the y-axis

- As the rule above reflection across the y-axis change the sign of x

∴ g(x) = f(-x)

∵ f(x) = x²

∴ g(x) = (-x)²

- Remember (-ve)^even number = (+ve)

∴ (-x)² = x²

∴ g(x) = x²

- The function g(x) is represent by upward parabola with vertex

 (0 , 0) (black graph in the attached picture)

∴ The graph of g(x) is the same with the graph of f(x)

- The red graph and the black graph are coincide