6: Polynomial Functions
- Page ID
- 19719
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- 6.1: Polynomial Functions
- The root word “poly” means “many,” as in polygon (many sides) or polyglot (speaking many languages—multilingual). In algebra, the word polynomial means “many terms,” where the phrase “many terms” can be construed to mean anywhere from one to an arbitrary, but finite, number of terms. Consequently, a monomial could be considered a polynomial, as could binomials and trinomials. In our work, we will concentrate for the most part on polynomials of a single variable.
- 6.2: Zeros of Polynomials
- In the previous section we studied the end-behavior of polynomials. In this section, our focus shifts to the interior. There are two important areas of concentration: the local maxima and minima of the polynomial, and the location of the x-intercepts or zeros of the polynomial. In this section we concentrate on finding the zeros of the polynomial.
- 6.3: Extrema and Models
- In the last section, we used end-behavior and zeros to sketch the graph of a given polynomial. We also mentioned that it takes a semester of calculus to learn an analytic technique used to calculate the “turning points” of the polynomial. That said, we’ll still pursue the coordinates of the “turning points” in this section, but we will use the graphing calculator to assist us in this quest; and then we will use this technique with some applications.