Concept explainers
To explain: What does the graph of the polynomial function tell you about the sign of the leading coefficient, the degree of the function, and the number of real zeros? Explain your reasoning.
The coefficient of the function is negative.
The given function is a 5th degree polynomial.
There are 5 real zeros for the given function.
Given information:
Graph of a polynomial function.
Formula used:
The x -intercepts of a function are the points where graph crosses the x -axis.
The degree of a polynomial function is one more than its turning points.
Calculation:
There are four turning points for the given graph. The degree of a polynomial function is one more than its turning points, therefore, the given polynomial is a 5th degree polynomial.
From the graph, it can be observed that the graph approaches positive infinity as x approaches negative infinity and graph approaches negative infinity as x approaches positive infinity. This means that the leading coefficient is negative.
From the given graph, it is visible that the graph crosses the x -axis 5 times, therefore, the function has 5 real zeros.
Chapter 2 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education