How Do You Calculate Intersection Points of Two Graphs?

[sam1390]

i have two graphs, i need to know how to calculate the points where the two graphs touch.

in my case there are two points.

do i have to make the equation equal or something?

the two equations are (7x)/(x^2+1)

and (x^2+2x+5)/(x+2)

 

[LowlyPion]

Welcome to PF.

You mean that you have 2 equations Y_(x).

And you want to identify where the values of Y are equal between the 2 equations.

Maybe if you set one = to the other and solved for x ...?

 

[thomate1]

To calculate the points where the two graphs touch, we need to find the values of x that satisfy both equations. This can be done by setting the two equations equal to each other and solving for x. In this case, we have:

(7x)/(x^2+1) = (x^2+2x+5)/(x+2)

We can then cross-multiply and rearrange the terms to get:

7x(x+2) = (x^2+1)(x^2+2x+5)

Expanding the terms on both sides, we get:

7x^2 + 14x = x^4 + 2x^3 + 5x^2 + x^2 + 2x + 5x + 10

Simplifying further, we get:

x^4 + 2x^3 - 2x^2 + 21x + 10 = 0

This is a fourth-degree polynomial equation, which can be solved using various methods (e.g. factoring, graphing, using a calculator). Once we have the solutions for x, we can plug them back into either of the original equations to find the corresponding y-values and determine the points where the two graphs touch.