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the scatterplot 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 we could fit a parabola to it if we could find a curve of best fit and that parabola might look something like might look something like it might look something like this again I'm just kind of estimating it trying to draw a parabola with my hand it's gonna be a hand 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 the other ones have a negative 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're 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 and what we have clear what we have here is clearly it looks looks like the right half of an upward-opening parabola so we could rule out the ones that are would be downward opening so we could rule out the ones that have a negative coefficient on the second degree second degree term 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 they have you know this is 201 verses point 201 264 verses 0.26 for 969 verses 0.9 69 and so we could really look at our curve right over here and and get a sense of and and test some points so if you look at maybe the easiest one 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 close close is going to be close to zero it's going to be definitely 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 the zero point nine six nine so y would be easier so this has the point zero comma zero point nine six nine on it which seems pretty close to our criteria that way we want when x is 0 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 why is 969 so here in order if you pick that if you picked if you picked this choice right over this is not close to zero this is nowhere 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 you can definitely rule this one out and we would be left with that choice right there and you could try other other points but that one would definitely be the easiest to evaluate