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

1 Answer
Mar 9, 2017

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]}