How many y-intercepts can a quadratic funtion can have ?

If your quadratic function has x intercepts of 4 and -3, that means that the points are (4, 0) and (-3,0), or the values x has when y=0. Since your quadratic (which represents y) must then equal 0, then your factors of that equation would potentially equal 0 as well. That means that if x=4, then subtract 4 from each side to get x-4=0, and so one factor is (x-4) Similarly your other factor would be (x+3). 

To get your quadratic, FOIL: 
(x-4)(x+3)=0 
x^2-x-12=0