MYTUTOR SUBJECT ANSWERS

767 views

How do I find the points of intersection between two curves?

This problem is a graphical representation of finding the solutions to a pair of simultaneous equations.

In this example we will use the curves y=2x2 , and y=x2+1. This is a very straightforward example, but demonstrates the method of finding the intersection of two curves well.

Step 1  - since the LHS of both these equations is the same (y=...) we can equate the two equations:

2x2=x2+1

This is a fairly easy equation to solve:

Lets make one side equal to zero:

-x+1=0

Lets move everything across to the other side to get rid of the minus signs.

x2 - 1 =0

This is the difference of two squares, so can be factorised:

(x+1)(x-1)=0

So the x-coordinates of the intersection points are  +1 and -1.

Step 2 - Now we need to find the y-coordinates. We do this by plugging the x-values into the original equations. We can use either one, because the lines intersect (so they should give us the same result!)

When x= +1, 

y=2x2

y=2(1)=2

When x= -1

y=2(-1)= 2

So the points of intersection have coordinates (-1,2) and (1,2)

We can see this graphically: (see how easy this example was!)

http://fooplot.com/plot/l26e9y97hd

Jacob R. A Level Chemistry tutor, A Level Physics tutor, A Level Math...

2 years ago

Answered by Jacob, an A Level Maths tutor with MyTutor


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

295 SUBJECT SPECIALISTS

£36 /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...”

£30 /hr

Venetia L.

Degree: General Engineering (Masters) - Durham University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“I study General Engineering at the University of Durham. I have always enjoyed maths and sciences, so hope to help students who share my love for them too!”

£36 /hr

Jacan C.

Degree: Theoretical Physics (Masters) - York University

Subjects offered: Maths, Science+ 3 more

Maths
Science
Physics
Further Mathematics
Chemistry

“Helping the striving and the struggling with caring, friendly and structured tuition. With 200+ hours of experience, offering Physics, Maths and Chemistry.”

About the author

£20 /hr

Jacob R.

Degree: Natural Sciences (Masters) - Cambridge University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
Chemistry

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

MyTutor guarantee

You may also like...

Other A Level Maths questions

Find the cartesian equation of a curve?

Express (√5+4)/(√5-2) in the form p+q√5 where p and q are integers.

How do I solve equations like 3sin^2(x) - 2cos(x) = 2

A rollercoaster stops at a point with GPE of 10kJ and then travels down a frictionless slope reaching a speed of 10 m/s at ground level. After this, what length of horizontal track (friction coefficient = 0.5) is needed to bring the rollercoaster to rest?

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