Question

How are the graphs `f(x)=x^2` and `g(x)=1/2x^2-5` related?

Answer 1

`f(x)` is the parent graph of `g(x)`. See below.

Explanation:

Basically, `f(x)` is the original graph , while `g(x)` is the result of `f(x)` after it went through transformations .

Notice how in `g(x)`, `x^2` (which is the same as `f(x)`) is stretched by a factor of `1/2` and moved downwards 5 units.

If we take away these two transformations on `g(x)`, it'll look like `f(x)`.