MYTUTOR SUBJECT ANSWERS

61 views

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

2 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

180 SUBJECT SPECIALISTS

£20 /hr

Matthew M.

Degree: Engineering Mathematics (Bachelors) - Bristol University

Subjects offered: Maths, Law+ 1 more

Maths
Law
History

“I am an Engineering Math student at the University of Bristol. I have a range of interests, which cover maths, history and law, and would love to help others in these areas as well as encourage the same enthusiasm I have in others! I a...”

MyTutor guarantee

£26 /hr

Matthew D.

Degree: Maths and Philosophy (Masters) - Durham University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“ I will make sure I am familiar with your specific exam board, and questions beyond this can of course be pursued in a tutorial too”

£30 /hr

Adam D.

Degree: Economics and Management (Bachelors) - Bristol University

Subjects offered: Maths, Economics

Maths
Economics

“I am a second year undergraduate student at the University of Bristol, studying Economics and Management. I achieved A* in Economics and Maths A-levels and an A* at maths GCSE so would be very happy to help any students who are studyi...”

About the author

£20 /hr

Dan S.

Degree: Mathematics & Statistics (Bachelors) - Warwick University

Subjects offered: Maths, Further Mathematics

Maths
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

How do I find the equation of the normal line given a point on the curve?

Solve x^2 + 8x +3 = 0 by completing the square.

Write tan(3x) in terms of tan(x). Hence show that the roots of t^3 - 3t^2 - 3t + 1 = 0 are tan(pi/12), tan(5pi/12) and tan(3pi/4)

How do I draw and sketch an equation?

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok