Polynomial end behavior example  Polynomial and rational functions  Algebra II  Khan Academy  Summary and Q&A
TL;DR
Determine which equations correspond to each graph by analyzing the end behavior and key characteristics.
Key Insights
 🤩 Analyzing end behavior and key characteristics helps identify the equations that correspond to specific functions.
 📈 The coefficients and signs of the highestdegree terms provide valuable information about the shape and end behavior of the graphs.
 Yintercepts can serve as additional evidence to confirm the matching of equations and graphs.
Transcript
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Questions & Answers
Q: How can we determine which equations match with each graph?
We can analyze the end behavior and key characteristics of the functions to match them with their corresponding equations.
Q: What is the equation for function g(x)?
The equation for function g(x) is y = 1/2x^2  9/2, which represents an upwardopening parabola with a yintercept at 9/2.
Q: How can we identify function h(x)?
Function h(x) is represented by the equation y = 1/10x + 3x^2  9, which is a thirddegree polynomial with end behavior similar to negative x cubed and a yintercept at 2.7.
Q: What equation defines function f(x)?
The equation y = 1/10x^4 + bx^3 + cx^2 + dx + 8.1 represents function f(x), a fourthdegree polynomial with end behavior similar to x squared and a yintercept at 8.1.
Q: How does analyzing end behavior help in matching equations with graphs?
Analyzing end behavior allows us to identify the polynomial degree and the sign of the leading coefficient, which provides essential clues to match equations with their corresponding graphs.
Summary & Key Takeaways

The video discusses three functions and three potential equations that could define them.

The first function, g(x), is an upwardopening parabola with a yintercept at 9/2.

The second function, h(x), is a thirddegree polynomial with end behavior similar to negative x cubed and a yintercept at 2.7.

The third function, f(x), is a fourthdegree polynomial with end behavior similar to x squared and a yintercept at 8.1.