Question

How is the graph of `g(x)=x^2+3` related to the graph of `f(x)=x^2`?

Answer 1

See both graphs in the same frame and compare.

Explanation:

Note that `y_g-y_a = x^2+3-x^2=3`.

From g to f, it is `(x, y) to (x, y+3)`.

Also, they are asymptotic to each other.

As `x to +-oo, y_g and y_f to oo`..

graph{(y-x^2)(y-x^2-3)=0 [-20, 20, -10, 10]}