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Basic Polynomial Graphs - Problem 3

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Teacher/Instructor Carl Horowitz
Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

Graphing a basic 4th degree polynomial so in this particular problem we are going to be dealing with x to the fourth and we have a table we are going to fill up some points and then plot them to see what this graph looks like.

So starting with -2, -2 to the fourth so we have 4 -2’s it’s going to cancel out to be an even number, 2 to the fourth is we get 2, 4, 8, 16, so we are going to be dealing with +6. -1 to the fourth again negatives will cancel out 1 to any power will just going to be 1. 0 to forth is 0, 1 to the fourth is 1 and 2 to the fourth is going to be the same as -2 to the fourth which is 16.

So from here we have some points on the graph of x to the fourth let’s plot this to figure out what this looks like. I’m not really concerned with precision I just want to get a rough idea of what this graph looks like. So we go to (-2,16) we go over 2 up 16 this is way off my graph but it's going to be somewhere up here roughly. (-1 1) going to be down here (0,0) (1,1) and then 2 and it's going to be way up here again. Connecting the dots or at least trying to, we are going to end up with a very steep 'u' graph.

Okay so this is what a basic fourth degree polynomial looks like. I do want to draw a quick comparison we do know the graph 2x² as well which we have right over here. We can a notice a few many similarities okay. They both go through the point (0,0), (1,1), (-1,1), but the x to fourth graph is significantly steeper so this basically sort of looks like an actual square graph sort of question, it’s going to be the same added for any even power, we have 2 4 6 8. Any power of x is going to be the same sort of shape the higher the degree the more squeezed then that graph becomes.

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