How is the graph of f(x)=x^2-4 related to the graph of f(x)=x^2?

2 Answers
Jul 20, 2018

f(x)=x^2-4 is the same graph, except the y-coordinates of each point are shifted down 4.

Explanation:

f(x)=x^2 is the parent function of a quadratic.

f(x)=x^2-4 is identical to the parent function, except for the -4 which is the y-intercept. So each coordinate, and therefore the whole graph is shifted 4 units down.

Jul 20, 2018

See below:

Explanation:

If we have a general function

f(x)=x^2+c, then c represents how much we move horizontally or vertically from the base function f(x)=x^2.

If c is positive, the graph has been shifted up, and if c is negative, the graph has been shifted down.

We can interpret f(x)=x^2-4 as the graph of x^2 shifted down by 4. This only changes the y values.

Hope this helps!