The idea of end behavior, or what the y values do as x gets really big to the right or really negative to the left, is a key idea as you move into higher math- all the way through calculus. The ends of any even degree polynomial will look like y = x^2 or y = - x^2 in terms of how both ends will go up or both go down. The ends of any odd degree polynomial will look like y = x^3 or y = - x^3 in terms of how one "arm" will go up and the other go down. Note that the degree and positive/negative leading coefficient both are considered when finding end behavior.
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