# How do you graph y = x^2 - 3?

May 29, 2018

See below

#### Explanation:

I'm assuming that you are familiar with the graph of $f \left(x\right) = {x}^{2}$, since it is the "standard" parabola:

graph{x^2 [-3, 3, -4.5, 10]}

Now, the function you want to graph is not exactly this one, but they're quite similar: $f \left(x\right) = {x}^{2} - 3$ is a transformed version of $f \left(x\right) = {x}^{2}$.

The tranformation belongs to the following family of transformations:

$f \left(x\right) \setminus \to f \left(x\right) + k$

(in your case, $k = - 3$)

This kind of tranformations translate the graph vertically, upwards if $k > 0$, downwards otherwise. So, in your case, there will be a shift of three units down. Compare this graph with the first one:

graph{x^2-3 [-3, 3, -4.5, 10]}

you can see how the "shape" is identical, and the only difference is the vertical translation.