 This video will talk about polynomial function applications. So we have this graph talking about water levels over a six month period and it wants to know what is the minimum degree? Oh we got one turn, two turns, three turns. So three turns means that I can have one more in my degree so it's degree four. How many months was the water level below normal in the six month period? Well this is normal. The x-axis is normal. So it's got, here's one month and then it's above for two to three and three to four and then from four to five that's below and from five to six is below so that gives us two. So we have a total of three months. And then in the same graph here at the beginning of the water level is 36 inches. That's going to be important to us later. And we want to then construct a model for this particular graph. You find your x-intercepts and that's going to be x minus one and x minus two and then we have another one at four so x minus four and we have another one at six so x minus six. Well here is where this comes in. We don't know what our a is but we do know that it is 36 inches when the m or in our case the x is zero. So if I plug zero in here and zero in here zero minus four and zero minus six we're going to have 36 is equal to if you multiply all that out you get 48a and when you divide 36 and 48 you end up with three fours. So our real function here is get my eraser. We're going to say not three not a but we want to have three fours and there we have our function. So now to answer the question use the model to determine the water level in months three and five we can plug in chug three and five but to be a little quicker I'm just going to come to my calculator I've already put in this equation into y equal so three months it was four point five and at five months it was negative nine. And if we go back up and look at the graph you can see that four point five would make sense here and negative nine would make sense at five months. The second problem we have a posh restaurant opens up at ten closes at nine and this is what the customer count is and all that's good stuff so we need our calculator because it says use the collected data to look at the scattergram and then determine the regression form and then find it. I've already put all that data in here but I will show you come over here to my calculator I've put all that data in and I went into y equal and I turned my plot on and this is really blank the way I have it set up so we're just going to look at our zoom nine and you can see you have one two three four five six data points just like we have one two three four five six data points there don't miss those ones that are near the x-axis so it really looks like kind of like an m so that makes me think that I have one two three turns so three turns means degree four and degree four is what we call a quartic a cubic is degree three and a quartic is degree four so go back over to stat and calculate and then court reg down here is seven and you find out you get this wonderful equation that I have plugged in and I'll write it for you here it's negative point three five seven is what I use t to the fourth plus seven point five three five t cubed minus forty nine point seven seven because it's six nine nine t squared plus one eleven point six eight seven and let me get rid of my quartic because I already told you that I can write it somewhere else later and that's t and then plus point zero to five when we round so we found a quartic and when we go and look at our graph here if I come down and I arrow over to the equal sign and press enter it will now show me my graph on top of my scatter gram and I get this wonderful little graph so it says use this equation and its graph to find what time it reaches its morning peak and its evening peak well those are going to be the maximum points here so second trace and max is four and we need to be to the left of one of our maxes and then to the right of it and when we do that it's going to give us a nice number enter and then go to the other side and enter enter for the guess and it says one point seven two and one point seven two is approximately and if I take 60 times point seventy is equal to forty three so we're going to have here one point seven two gives us eleven forty three and then if we go do the other one second trace four and we find out that this one is nine point one three one four six those go to our screen again sixty times point one four is going to give us about seven oh eight for the time and then I give you the graph so that we can not have to necessarily work with the calculator although we can what time does the business is the slowest so that's going to be this point down here and we better go to my graph the second trace we went the minimum this time to come back and go to the left of that minimum and enter and go to the right of that minimum and enter and then enter for the guess and we find out that that is four point nine eight so we could do four point nine eight or we could just round it approximately five hours which translates to three p.m. and then we want to know how many customers there are what that would be thirty two point nine so let's please call that thirty three and then the last one I want to come back to my calculator white equal and enter down to why to and call that white one hundred customers are my wise so I'm going to look at this graph and see the intersections and second trace five enter enter enter will get me the first one and that tells me that it's at about seven point eight seven hours or this call that eight hours I think the book doesn't round it but we're going to round it and then second trace five and I want to go to the other one so enter enter enter and we find out that there are also a hundred serve customers at ten hours later so we can say between the hours of six which is the eight hours later and eight which is a ten hours later they would have a hundred customers or more because it does go above that between those two hours