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### Course: Algebra (all content)>Unit 10

Lesson 34: End behavior of polynomial functions

# Intro to end behavior of polynomials

Sal explains what "end behavior" is and what affects the end behavior of polynomial functions. Created by Sal Khan.

## Want to join the conversation?

• Sal keeps saying "really really negative" and "less negative" "more positive. What does that mean?
• More negative means the polynomial's line is moving downward. Less negative or more positive would indicate the line is moving upward.
• how I do this in real-time?
• You look at the highest exponent and check the sign of the leading coefficient. If the exponent is even or odd, that will show whether or not the ends will be together or not. Next if the leading coefficient is positive or negative then you will know whether or not the ends are together or not. Remember: odd - the ends are not together and even - the ends are together.
• I'm trying to do the practice questions on here but it's multiple-choice. And the answers look very different from what the dude is talking about in this video. How does the infinite symbol involve this stuff?
• at sal talks about the middle of the polynomial function doing some "funky stuff" in the middle. is there a video or a link that you can share with me so as to get some insight on this middle behavior?
• wouldn't it be helpful if you started with linear equations since they are easier to remember and they also follow the same pattern.
• what is a polynomial?
• That's a question that puts me through meriormies of Khan talking. You probably should start at Lesson 1: Multiplying monomials by polynomials
• Could anyone explain to me how to find the zeros of polynomial functions? I know the zeros indicate a change in direction, but I'm not exactly clear on how to find them. Possible explanation or video explanation would help a ton! Thank you
• Can someone give me a video on khanacademy where he show us how the sides can be opposite or the same?
• You would have to do a search to see if there is a video. Or, do an internet search for videos.

You should learn the basic patterns for different types of equations. There are simple equations / functions called parent functions.

y=x^2 is a quadratic. It always creates a parabola. The left and the right sides of the parabola will always go to +infinity. If you have y=-x^2, then the left and right sides of the parabola go to -infinity. So, basically both sides always move in the same direction.

y=x^3 is a cubic equation. The left side goes to -infinity and the right side goes to -infinity. If you have y=-x^3, then the sides flip. The left side rises to +infinity and the right side goes to -infinity. Basically the end values move in opposite directions.

The highest degree of polynomial equations determine the end behavior.
-- If the degree is even, like y=x^2; y=X^4; y=x^6; etc., then the ends will extend in the same direction.
-- If the degree is odd, like y=x^3; y=x^5; y=x^7; etc., then the ends will move in opposite directions.

Hope this helps.
• End behavior tells you what the value of a function will eventually become. For example, if you were to try and plot the graph of a function `f(x) = x^4 - 1000000*x^2` , you're going to get a negative value for any small `x`, and you may think to yourself - "oh well, guess this function will always output negative values.". But that's not so. `x^4` will inevitably become greater than `1000000*x^2` at some point, and the outputs of the function will become positive. And as `x` become larger and larger, the function will be approaching +inf. That's what end behavior is.