# How do I plot y=x^2-1?

To plot any graph, you need to find out where the curve cuts the x and y-axis, and where it's stationary points are, aswell as what type of stationary point you have.

Here are the steps:

__1) Let x=0; find where the curve passes the y axis.__

Here, y =-1. This means the curve passes the y axis at (0,-1)

__2) Let y=0; find where the curve passes the x axis.__

Here we get 0=x^{2}-1

So x^{2}=1

The square roots of 1 are: 1 and -1. (1x1=1, -1x-1=1)

This means the curve crosses the x axis as (-1, 0) and (1,0).

*Remember the order of this equation (the highest power to which a x is raised) gives the number of times the curve crosses the x axis, here it is two. (This is the same for the y axis. Here, there order of y is 1, so the curve passes through the y axis 1 time.*

__3) Differentiate the equation with respect to x and make this equal to 0; find the stationary points.__

dy/dx =2x=0

This tells us there is a stationary point at x=0. We know from step 1 that this corresponds to the coordinate (0, -1).

For the curve to pass through all of these points, it might be clear that the graph is a "sad face", passing through (0, -1), (1, 0) and (-1, 0) with the __MINIMUM __located at (0,-1)

However, if this is not clear to you, difference the equation again with respect to x. If this gives you a postive answer, you have a minimum, a negative answer means you have a maximum.

__4) Differentiate again with respect to x to find the second derivative; does this give you a postive answer?__

Here, d^{2}y/dx^{2}= 2.

Obviously this is a postive number meaning you have a minimum.