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

JR
Answered by Jacob R. Maths tutor

152717 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How do I find the limit of a sequence that is expressed as a fraction?


Integrate (3x^2+2x^-1) with respect to x in the range of K to 3 and explain why K cannot be 0


Let f(x)=xln(x)-x. Find f'(x). Hence or otherwise, evaluate the integral of ln(x^3) between 1 and e.


How do you find the gradient of a line at a certain point when f(x) is in the form of a fraction, where both the numerator and denominator are functions of x?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences