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) moved 6 units down.

`x^2" has a minimum at " (0,0)`

`x^2-6" has a minimum at "(0,-6)`

`•"In general for "y=x^2+c`

This is the graph of `x^2"` moved vertically up/ down by c units

`• " If "c>0" then move up "uarr`

`• " If "c<0" then move down "darr`

Here is the graph of `f(x)=x^2`
graph{x^2 [-10, 10, -5, 5]}

and the graph of `g(x)=x^2-6`
graph{x^2-6 [-16.01, 16.02, -8, 8.02]}