Question

How do i write an absolute equation with the solution of 2 and 6

Answer 1

Absolute graphs are sort of like quadratics:



In which they have a vertex, and symmetry.

there are multiple ways to make an equation that gets the same answer, but here is the standard formula for absolute:

y = a|x-h|+k

a= slope
vertex = (h,k)

In order to have two answers, then you have to include a line, making it a system of equations:



y = some constant

Set the equations equal to each other:

a|x-h|+k = some constant

And you get the answer.

Answer 2

"But hold on!" you might say. "You didn't answer my question!"

Let's pull up that graph again:



We need an equation that has two intersections, with x coordinates equaling to 2 and 6

First, find the vertex. (Remember, absolute value is the distance between something.):



We must set the vertex so that that the x coord. has an equal distance from 2 than it does from 6:

Use some your brains and you get 4 for the x coord. For the y, I would pick 0 for y and 1 for slope, since it is easiest to work with.

Now we have:

y = |x -4|

Now for the line.



Now we see that the line is y = 2

So:

|x-4| = 2 would be a possible answer.

(That was alot of typing)