Write the equation of the rational funtion given the horizontal asymptote y=0, x-intercept at (-4,0) y-intercept at (0,-8) and vertical asymptotes x=-7 and x=-8. I need to know how to find the 'a', I've been at this for hours and I've emailed my teacher but no advice seems to help.

f(x)= a(x+4)/(x+7)(x+8)

Question

Write the equation of the rational funtion given the horizontal asymptote y=0, x-intercept at (-4,0) y-intercept at (0,-8) and vertical asymptotes x=-7 and x=-8. I need to know how to find the 'a', I've been at this for hours and I've emailed my teacher but no advice seems to help.

f(x)= a(x+4)/(x+7)(x+8)

cruffo · Answer

Looks like the hint is the y-intercept.  To get the y-intercept, plug in 0 for x.  Then
$$\frac{a(0+4)}{(0+7)(0+8)} = \frac{4a}{56} = \frac{a}{14}$$
So you need this to be -8.  Solve
$$\frac{a}{14} = -8$$
$$a = -112$$