Find vertical axis horizontal axisslope x intercept and y in

Find vertical axis, horizontal axis/slope, x intercept and y intercept.

2x^2+x-6/x^2+3x+2

y = (2x^2+x-6)/(x^2+3x+2)

x intercept plug y = 0

0 = (2x^2+x-6)/(x^2+3x+2)

2x^2+x-6 = 0

(x+2)(2x-3) = 0

x = -2 , x = 3/2 ----- x intercepts

y intercept , plug x = 0 in the function

y = (2x^2+x-6)/(x^2+3x+2)

y = -6 / 2 = -3

y = - 3 ( y intercept )

vertical asymptotes

set denominator = 0

x^2+3x+2 = 0

x = -1 ( vertical asymtote)

horizontal asymptote

y = coefficient of x^2 in numerator / coefficient of x^2 in denominator = 2 / 1

y = 2 ( horizontal asymtote)