in this video you're going to learn how to write a cubic function when you're giving the zeros or the x-intercepts or a graph like this so how exactly do we write a cubic equation well the important thing to remember is that when you're given these x-intercepts like this you want to understand the connection between the zeros the x-intercepts the roots the solutions those all mean the same thing but what we're interested in is the factors and what a factor is it's ax minus whatever the zero is or the x-intercept so in this case the factor would be x minus negative three which is x plus 3 this factor here because it crosses at one is going to be x minus one and then because this x-intercept is 4 it's going to be X minus 4 now the only other thing we need to add to this equation is a coefficient a and what the a does is it stretches the graph or compresses the graph and so we're trying to figure out you know like what's the graph that goes through these three x-intercepts but also goes through it like a fourth point that's not on the x-axis and what we do is we plug in those values x and y in for x and y here so we can solve for that vertical stretch or vertical shrink so in this case x is 0 so let's go ahead and put 0 in for each of these X's and y equals 2 so let's put 2 and for y here and we're going to solve for a so we have 2 equals a 0 plus 3 is 3 0 minus 1 is negative 1 and 0 minus 4 is negative 4 if we multiply that together we get positive 12 a equals 2 and if we divide both sides by 12 to get a by itself you can see that a is equal to 1/6 and all we have to do now is put it back in for a and that's going to be our cubic equation now if you want to take it one step further you can multiply all this out and then also multiply it by the 1/6 and that'll be you know completely like simplified but here we can leave it in the factored form and that'll be a pretty good way to write it so that's how you would write cubic functions I hope this video helped you I'll see you in the next video