Polynomial end behavior example | Polynomial and rational functions | Algebra II | Khan Academy | Summary and Q&A

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December 19, 2013
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Polynomial end behavior example | Polynomial and rational functions | Algebra II | Khan Academy

TL;DR

Determine which equations correspond to each graph by analyzing the end behavior and key characteristics.

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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 upward-opening parabola with a y-intercept 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 third-degree polynomial with end behavior similar to negative x cubed and a y-intercept 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 fourth-degree polynomial with end behavior similar to x squared and a y-intercept 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 upward-opening parabola with a y-intercept at -9/2.

  • The second function, h(x), is a third-degree polynomial with end behavior similar to negative x cubed and a y-intercept at 2.7.

  • The third function, f(x), is a fourth-degree polynomial with end behavior similar to x squared and a y-intercept at 8.1.

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