Sketch the curve y = (x^2 - 9)(x - 2)

When it comes to curve sketching, there are a number of tests that you can do to find out crucial characteristics about the curve. They are following:

1. Setting x = 0 will give you the points at which the curve hits the y-axis. In our example we have y = (0 - 9)(0 - 2) = 18, hence it hits the y-axis at the point y = 18.

2. Setting y = 0 will give you the points at which the curve hits the x-axis. In our example we have
(x^2 - 9)(x - 2) = 0
(x + 3)(x - 3)(x - 2) = 0
Hence it hits the x-axis at x = -3, 2, 3.

3. Solving the equation dy/dx = 0 will give the x-coordinates of the stationary points of the curve. In our example we have
y = (x2 - 9)(x - 2)
y = x- 9x - 2x2 + 18
dy/dx = 3x2 - 9 - 4x
(Setting dy/dx = 0)
3x2 - 4x - 9 = 0
(This can be solved using the quadratic formula)
x = ( 4 +- (16 - 4*3*(-9))1/2 )/( 2*3 )
x = -1.189 or x = 2.523
Hence there are stationary points here.

4. Finally, it is useful to see how y behaves when x tends to plus infinity and minus infinity. In our example, we can see that as x goes to plus infinity we also have (x- 9) goes to infinity and (x - 2) goes to infinity. As a result, y goes to plus infinity. Also, we can see that as x goes to minus infinity we have (x- 9) goes to plus infinity and (x - 2) goes to minus infinity. As a result, y goes to minus infinity.

From these tests we can gain enough information in order to sketch the curve.

Dan S. A Level Maths tutor, A Level Further Mathematics  tutor

4 months ago

Answered by Dan, who has applied to tutor A Level Maths with MyTutor

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


£20 /hr

Steven K.

Degree: Material Science (Masters) - Oxford, The Queen's College University

Subjects offered: Maths, -Personal Statements-

-Personal Statements-

“I started tutoring through my father who is a maths teacher, as he would pass on requests for lessons to me. Through my A levels I tutored GCSE maths, and began to also teach physics, chemistry and biology, the other subjects i was st...”

£20 /hr

Sajidah H.

Degree: Mathematics (Bachelors) - Birmingham University

Subjects offered: Maths, Further Mathematics + 2 more

Further Mathematics
-Personal Statements-

“I am a Mathematics student at the University of Birmingham. I have a genuine love for Maths and eventually want to go on to teach it to young people. I am friendly and very patient, and if you’re struggling, we’ll work together to fin...”

MyTutor guarantee

£20 /hr

Aashish M.

Degree: Mechanical Engineering (Masters) - Bath University

Subjects offered: Maths, Physics+ 2 more

Further Mathematics

“I am a Mechanical Engineering student, currently studying at the University of Bath. I enjoy doing Maths and Science, so if you're struggling with a problem, I would be happy to help! During the session, I'll go through the content wit...”

MyTutor guarantee

About the author

£20 /hr

Dan S.

Degree: Mathematics & Statistics (Bachelors) - Warwick University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Posts by Dan

Find the gradient of the line 4x+9y=10.

Given that 4(cosec x)^2 - (cot x)^2 = k, express sec x in terms of k.

Sketch the curve y = (x^2 - 9)(x - 2)

Other A Level Maths questions

What is the gradient of y = xcos(x) at x=0?

Using logarithms solve 8^(2x+1) = 24 (to 3dp)

How do you intergrate sin^2(x)?

How can I find the area under the graph of y = f(x) between x = a and x = b?

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