MYTUTOR SUBJECT ANSWERS

409 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...

1 year ago

Answered by Jacob, an A Level Maths tutor with MyTutor

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

185 SUBJECT SPECIALISTS

£30 /hr

Fahad M.

Degree: Medicine And Surgery - MBChB (Bachelors) - Birmingham University

Subjects offered: Maths, Psychology+ 7 more

Maths
Psychology
Physics
Chemistry
Biology
.UKCAT.
.BMAT (BioMedical Admissions)
-Personal Statements-
-Medical School Preparation-

“About MeGraduating highschool with many distinctions I went on to become a medical student at the University of Birmingham. Having excelled in my interview (gaining the top rank in Motivation and Experience) I went on immediately to ...”

£24 /hr

Joe M.

Degree: Biology (Bachelors) - Durham University

Subjects offered: Maths, Science+ 2 more

Maths
Science
Chemistry
Biology

“Second year Biology student tutoring science and maths in a relaxed and friendly environment”

£20 /hr

Guy P.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics + 2 more

Maths
Further Mathematics
.STEP.
.MAT.

“About:Hi. I am a 2nd Year Mathematics student at the University of Warwick. I achieved a comfortable First in Year 1 and have continued this trend into my second year. Even from an early age, I have had a burning passion to engage m...”

About the author

£20 /hr

Jacob R.

Degree: Natural Sciences (Masters) - Cambridge University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
Chemistry

“1”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Find the area bounded by the curve x^2-2x+3 between the limits x=0 and x=1 and the horizontal axis.

What is the integral of sin^2(x)?

Using Trigonometric Identities prove that [(tan^2x)(cosecx)]/sinx=sec^2x

How do I find the angle between 2 vectors?

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