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=x2-1 

   So  x2=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, d2y/dx2= 2. 

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


Laura P. A Level Maths tutor, GCSE Maths tutor

1 year ago

Answered by Laura, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


Viktoriya L. A Level Accounting tutor, GCSE Accounting tutor, A Level...
View profile
£20 /hr

Viktoriya L.

Degree: accounting and finance (Bachelors) - LSE University

Subjects offered: Maths, Russian+ 5 more

-Personal Statements-

“Hello, My name is Viktoriya. I am a first year student at the London school of Economics and Poliical science studying accounting and finance. I am passionate about maths and finance in particular and wish to convey this passion to yo...”

MyTutor guarantee

Tom H. A Level Economics tutor, A Level Maths tutor, A Level Spanish ...
View profile
£24 /hr

Tom H.

Degree: Economics (Bachelors) - Durham University

Subjects offered: Maths, Spanish+ 3 more

Business Studies

“Top tutor from Durham University, ready to help you improve your grades, all the way to A*.”

PremiumZeeshan A. GCSE Maths tutor, A Level Physics tutor, A Level Maths tut...
View profile
£24 /hr

Zeeshan A.

Degree: Theoretical Physics with Applied Maths (Masters) - Birmingham University

Subjects offered: Maths, Physics+ 1 more

Further Mathematics

“Theoretical Physics w/ Applied Maths. I'd love to help with Maths and Physics.”

About the author

Laura P. A Level Maths tutor, GCSE Maths tutor
View profile
£20 /hr

Laura P.

Degree: Aerospace Engineering (Masters) - Bristol University

Subjects offered: Maths


“As an Aerospace Engineering student in Bristol University, I am passionate about Mathematics and Science. Allow me to help you improve your grades, and hopefully inspire along the way!”

You may also like...

Other A Level Maths questions

How do you take the derivative of a^x ?

How do you integrate the function cos^2(x)

Find the solution(s) of 3(x^2)-6x+2=0

Find the coordinates of the minimum point of the curve y = 3x^(2) + 9x + 10

View A Level Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss