Questions and Answers
Classify -6x^5+4x^3+3x^2+11 by degree.
quintic
Write -2x^2(-5x^2+4x^3) in standard form.
-8x^5 + 10x^4
What is the end behavior of the graph for the leading term 2x^7?
Down and up
How many turning points are there in the graph of y=2x-x^3?
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Interpret the variable h in the polynomial expression for the volume of a bottle, 4/3πr^2h.
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Study Notes
Polynomial Function Classification
- The polynomial -6x^5 + 4x^3 + 3x^2 + 11 is classified as a "quintic" due to its highest degree term being of exponent 5.
Standard Form Conversion
- The expression -2x^2(-5x^2 + 4x^3) simplifies to standard form as -8x^5 + 10x^4.
End Behavior of Polynomial Functions
- The leading term 2x^7 indicates an odd degree (7) with a positive leading coefficient, leading to down behavior on the left and up behavior on the right side of the graph.
Turning Points in Graphs
- The graph of the function y = 2x - x^3 has two turning points, occurring as the curve transitions from down to up and back down again.
Volume of a Bottle Representation
- In the polynomial expression for the volume of a bottle, 4/3πr^2h, the variable h signifies the overall height of the bottle, reflecting its vertical dimension in the context of the scenario.
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Description
Master the concepts of polynomial functions with these flashcards from Algebra Unit 1.1. Each card covers key topics such as classifying degrees, writing polynomials in standard form, and analyzing end behavior of graphs. Perfect for quick review and exam preparation.
