Scatterplots — Harder example

- [Instructor] The scatter plot drawn above, we'll take a look at it after we finish reading the question, depicts the average annual United States per capita consumption of high fructose corn syrup between the years 1970 and 1985. Which of the following functions best describes the relationship shown? So when we look at the scatter plot, we see that it definitely looks like we could fit a parabola to it. We could find a curve of best fit, and that parabola might look something like this. Once again, I'm just kinda estimating it, trying to draw a parabola with my hand. This is gonna be a hand-drawn parabola, but it's gonna look something like that. And what they're saying is, look, they've given us some candidates, some quadratic functions that would describe this curve of best fit or this parabola of best fit. And so which of these could it be? Well, there's a couple of things that you might immediately see. The first is is that a couple of these choices have a positive coefficient on the highest degree term, on the second degree term. And then the other ones, have a negative coefficient on the highest degree term. Well, if you have a positive coefficient on the highest degree term, on the second degree term, and if we were talking about a quadratic, you're going to have an upward opening parabola, and if you had a negative coefficient, it would be a downward opening parabola. What we have here is clearly, it looks like the right half of an upward opening parabola. So we could rule out the ones that would be downward opening. So we could rule out the ones that have a negative coefficient on the second degree terms. So let's rule those out right over here. And then when we look at the remaining two, we see there's a fairly dramatic difference in them. This is 201 versus .201. 264 versus .264. 969 versus .969. And so we could really look at our curve right over here and get a sense of and test some points. So if you look at or maybe the easiest way is to actually test when x is equal to zero. So when x is equal to zero, depending on how we draw our curve, our y is going to be pretty low. Our y is going to be close to zero. I'll just write is going to be close to zero. It's going to definitely be below five. It's gonna be probably definitely below two. So let's see which of these choices describe that. So when x is zero here, this term goes away, this term goes away, and we're left with 0.969. So y would be, so this has a point zero, 0.969 on it, which seems pretty close to our criteria that hey, we want when x is zero y is pretty close to zero. Let's see this one. This choice right over here, when x is zero, this term goes away, this term goes away. Y is 969. If you picked this choice right over, this is not close to zero. This actually would be off the charts right over here, the point zero, 969. It wouldn't even fit on that graph. So you can definitely rule this one out, and we would be left with that choice right there, and you can try other points, but that one would definitely be the easiest to evaluate.