I got 2(x-2)/(x+2)(x-4) but when I plugged it in, it wasn't the same graph.

The characteristics I got were

VA: x=-2,4

HA: y=0

x int: 2

y int: 1/2

maryeverdon Nov 10, 2020

#1**+1 **

You are on the right track

Certainly a part of the denominator must be (x+2)(x-4)

And given that (2,0) is on the graph, the numerator must have (x-2) in it.

Plus it looks a bit like a parabola, with a double root at x=2 so i suspect the numerator will be squared (I am not so sure that my logic is sound here)

Anyway so far I am thinking that it might be ..

\(y=\frac{k(x-2)^2}{(x+2)(x-4)}\\\) where k is a constant.

It looks like it might go through (0, 0.4)

when x=0

LHS= 4k / -8 = -k/2

-k/2=0.4

k=-0.8

So maybe it is

\(y=\frac{-0.8(x-2)^2}{(x+2)(x-4)}\\\)

check:

This is certainly not completely correct but the diagram you have provided is not very good.

This is probably close enough.

Maybe -1 would have looked a little closer than -0.8 . The the y intercept would have been 0.5

Melody Nov 11, 2020