# How do you graph (-2x^2)/(3x+6) using asymptotes, intercepts, end behavior?

Jan 17, 2017

Slant asymptote: $2 x + y - 4 = 0$ Vertical asymptote { $\uparrow x = - 2 \downarrow$
. The asymptotes design proximity ( getting the graph closer ), as the end behavior. x-intercept:2sqrt2. y-intercept: 8.

#### Explanation:

By actual division,

it is $y = - 2 x + 4 - \frac{8}{x + 2}$, giving the form

$\left(y + 2 x - 4\right) \left(x + 2\right) = 8$ that represents a hyperbola having

$\left(y + 2 x - 4\right) \left(x + 2\right) = 0$ as asymptotes,

meeting at the center $C \left(- 2 , 8\right)$.

The asymptotes design proximity ( getting the graph closer ), as the

See the asymptotes-inclusive Socratic graph.

x-intercept ( y = 0 ) :2sqrt2.

y-intercept ( x = 0 ) : 8 : 8

graph{((y+2x-4)(x+2)-8)((y+2x-4)(x+2+.0001y))=0 [-20, 40, -10, 20.]}