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## Algebra 2

### Course: Algebra 2>Unit 5

Lesson 4: Putting it all together

# Polynomial graphs: FAQ

## What are the "zeros" of a polynomial?

The zeros of a polynomial are the x-values where the polynomial crosses the x-axis. In other words, they're the points where the polynomial equals $0$.

## What do "positive and negative intervals" mean in the context of polynomials?

Polynomials can be positive or negative in certain intervals. For example, a polynomial might be positive for all $x$-values less than $-2$, negative between $-2$ and $3$, and positive again for all $x$-values greater than $3$.

## What is "end behavior" when it comes to polynomials?

The end behavior of a polynomial tells you what the polynomial "looks like" as it approaches positive and negative infinity. For example, if a polynomial "increases without bound" as $x$ approaches positive infinity, it means the polynomial keeps getting higher and higher on the graph the further to the right you go.

## Where are these concepts used in the real world?

Polynomials are used in a variety of real-world applications, from engineering to economics. For example, in physics, polynomials can be used to model the trajectory of an object in motion. Understanding the zeros, positive and negative intervals, and end behavior of a polynomial can help us understand the shape of the graph and make predictions about the system it models.

## Want to join the conversation?

• Who came up with math
• so real
• You need math for the future is what people tell me all the time

Why do we have to do these problems for math??
• I'm a financial engineer, my whole salary comes from mathematical foundations like this which build up to more complex specific topics, therefore, my whole family's life too. I too was told when I was young that this stuff is not necessary and won't be used, and because of that I had to go learn it all when I was in uni. Save yourself the time, study it well now, it will pay off greatly!!
• im confused on how to idenity the end behaviors of polynomials
• Firstly, look at the first-degree polynomial in the graph, should look like y=axⁿ

If "n" is even the graph will approach only +∞ or -∞, kind of like a quadratic function.
If "a" is positive and "n" is even, the graph will approach +∞ when "x" approaches ±∞.
If "a" is negative and "n" is even, the graph will approach -∞ when "x" approaches ±∞.

However, things get a little complicated when "n" is odd. Think of a cubic function and how one direction leads to +∞ while the other leads to -∞.

If "a" is positive and "n" is odd, then "y" will approach the same direction as "x". When "x" approaches +∞ "y" will approach +∞. If "x" approaches -∞, then "y" will also approach -∞.
If "a" is negative and "n" is odd, then "y" will approach the opposite direction as "x". When "x" approaches +∞ "y" will approach -∞. If "x" approaches -∞, then "y" will approach +∞