Find an expression for a rational function f(x) that satisfies the conditions: a horizontal asymptote at y = 4, vertical asymptotes at x = ±2, and contains the point (0, −3).

precalc.
answers attached.

Ok, for the vertical asymptote to the either ±2, that simply means, the denominator =0 must give thus roots, thus 

so, that'd be the denominator

for the horizontal asymptote to be 4, or 4/1, we can simply make both numerator and denominator the same degree, and with leading coefficient of 4/1 respectively  thus 

now, that equation must have a point of ( 0 , -3 ), so the graph has to have such point, meaning, when y = -3, x = 0, so let's do that then, and let us add a coefficient of "a"