Question

How is the graph of `g(x)=x^2+6` related to the graph of `f(x)=x^2`?

Answer 1

`"see explanation"`

Explanation:

`"the graph of g(x) is the graph of f(x) shifted vertically by"`
`"+ 6 units"`

`"or equivalent to a translation "((0),(6))`

`"in general "`

`g(x)=x^2+-a`

`"for "a>0 " shift is "((0),(a))uarr`

`"for " a<0" shift is "((0),(-a))darr`

graph{(y-x^2)(y-x^2-6)=0 [-20, 20, -10, 10]}