# How do you find the asymptotes for #y=(2x^2-3x+4)/(x+2)#?

##### 1 Answer

Dec 15, 2016

Slant asymptote+

Vertical asymptote:

Illustrative graph is inserted.

:

#### Explanation:

By actual division,

Reorganizing,

This represents a hyperbola.(https://socratic.org/precalculus/functions-defined-and-notation/asymptotes)

Note that the equation of a hyperbola with asymptotes as the pair

of lines

(y-m x-c)(y-m' x-c') = 0 is

(y-m x-c)(y-m' x-c') = k and here it is

Also, the only conic with asympiotes is hyperbola.

The center of the hyperbola is the point of intersection of the

asymptotes,

graph{((y-2x+7)(x+2)-18)(y-2x+7)(x+1.99)(x+2.01)=0[-20 20 -40 20]}