Write an equation for a rational function with the given characteristics.

Vertical asymptote at

x = 4,

double zero at

x = 1,

y-intercept at

(0, 3)

y =

The vertical asymptote requires a factor of (x-4) in the denominator.

The double zero requires a factor of (x-1) ² in the numerator.

At x=0, these factors will give a value of (-1) ² / (-4) = - 1/4, so another constant factor of - 12 is needed to make the y-intercept be 3.

Your rational function is ...

... y = - 12 (x - 1) ² / (x - 4)