PPT-Finding Zeros Given the Graph of a Polynomial Function

Chapter 56 Review Zeros of Quadratic Functions In the previous chapter you learned several methods for solving quadratic equations If rather than a quadratic equation we think about the function . Copy the coordinate plane with the following information.. Simplify each expression.. 4) (x + 5) + (2x + 3) . 5) (x + 9) – (4x + 6) . 6) (-x. 2. – 2) – (x. 2. – 2) . X.  - . f(x) - . Objectives: Identify Polynomial functions. Determine end behavior recognize characteristics of polynomial functions. Use factoring to find zeros of polynomial functions.. Polynomials of degree 2 or higher have graphs that are smooth and continuous. By smooth we mean the graphs have rounded curves with no sharp corners. By continuous we mean the graphs have no breaks and can be drawn without lifting your pencil from the rectangular coordinate system.. Unit . 3. Polynomial Functions. Section: . 5.1. Polynomial Functions . This section studies the . Polynomial Function. .. Your Goal - learn to . identify. the function components that lead to its . Algebra 2. Chapter 5. This Slideshow was developed to accompany the textbook. Larson Algebra 2. By Larson. , R., Boswell, L., . Kanold. , T. D., & Stiff, L. . 2011 . Holt . McDougal. Some examples and diagrams are taken from the textbook.. Defn. : . Polynomial function. In the form of: . ..  . The coefficients are real numbers.. The exponents are non-negative integers.. The domain of the function is the set of all real numbers.. Taylor Johnson. (Taylor.Johnson@kctcs.edu). Elizabethtown Community . & . Technical College. Tools for Searching for Zeros . (1) Remainder Theorem. (2) Factor Theorem. (3) Intermediate Value Theorem. Section 4.5 beginning on page 190. Solving By Factoring. We already know how the zero product property allows us to solve quadratic equations, this property also allows us to solve factored polynomial equations [we learned how to factor polynomial expressions in the previous section].. Now, we have learned about several properties for polynomial functions. Finding y-intercepts. Finding x-intercepts (zeros). End behavior (leading coefficient, degree). Testing values for zeros/factors (synthetic division) . What do we already know about polynomial functions?. They are either ODD functions. They are either EVEN. functions. Linear. y = 4x - 5. Cubic. y = 4x. 3. - 5. Fifth Power. y = 4x. 5. –x 5. Quadratics. Objectives:. To approximate . x. -intercepts of a polynomial function with a graphing utility. To locate and use relative . extrema. of polynomial functions. To sketch the graphs of polynomial functions. Standard 15. Graph and analyze polynomial and radical functions to determine:. Domain and range. X and y intercepts. Maximum and minimum values. Intervals of increasing and decreasing. End behavior. With the function: f(x) = . What do we already know about polynomial functions?. They are either ODD functions. They are either EVEN. functions. Linear. y = 4x - 5. Cubic. y = 4x. 3. - 5. Fifth Power. y = 4x. 5. –x 5. Quadratics. What do we already know about polynomial functions?. They are either ODD functions. They are either EVEN. functions. Linear. y = 4x - 5. Cubic. y = 4x. 3. - 5. Fifth Power. y = 4x. 5. –x + 5. Quadratics. Lesson. Check: . . Worksheet Complex Numbers. Side 37 all. Side 38 (x4). . 2.5. Objective: . Find all real and complex zeros of a polynomial function..