Finding the equation of a graph?

Question

How do you find the equation of a graph when given three x-intercepts?

For example, the x-intercepts of this particular question are at x=-2, x=4, and x=6. How would I find the equation of it?

Answer 1

(x+2)(x-4)(x-6)

Answer 2

There are an infinite amount of equations that fit those x-intercepts.

Answer 3

If its linear then its x = 0

if you want a polynomial graph, those are your zeros

and the equation would be

y = (x + 2) ( x - 4) ( x - 6)

Answer 4

One way to do it is to set up the equation y = (x + 2)(x - 4)(x - 6).  When y=0, you get the three solutions for the x-intercepts.  So just take y = (x + 2)(x - 4)(x - 6) and expland the right side.

Of course, there are an infinite amount of equations that could have those three points for x-intercepts, but this is one of them.

Answer 5

If it can be assumed to be a straight line, then the equation is y = 0. Otherwise, there isn't enough information.

Answer 6

The best way to do any problem like this is take your x-intercepts say y1, y2, and y3. and subtract each from x and multiple:

(x-y1)*(x-y2)(x-y3) = eq that goes through each intercept

so,

(x+2)*(x-4)*(x-6) = x^3-8x^2+4x+48

ta-da!