Question

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

Answer 1

`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.

Answer 2

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!