1 / 4

Maximizing Volume of a Box and Polynomial Function Exploration in Advanced Algebra II

In this lesson, we explore higher-degree polynomials through practical applications. We start with an example involving a cardboard square measuring 30 inches by 30 inches, where we determine the height that maximizes the volume of a box cut from it. We will write a volume equation, graph the function, and identify local maxima and minima, discussing their characteristics. Additionally, we analyze polynomials with specific x-intercepts and coefficients, culminating in an assignment that reinforces these concepts through problem-solving.

robert-ellis
Télécharger la présentation

Maximizing Volume of a Box and Polynomial Function Exploration in Advanced Algebra II

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Advanced Algebra II Notes 7.7 Higher-Degree Polynomials Example 1: A box is cut from a square of cardboard which is 30 inches by 30 inches. What height will maximize the volume of the box? a) Write an equation for the volume of the box. Remember that the volume of a prism is: V = lwh b) Graph the function and determine the height which maximizes the volume.

  2. c) Find the local maximum and local minimum. Why are they LOCAL max and min and not absolute max and min? d) What is the end behavior of the polynomial? How could we predict this before graphing it?

  3. Example 2: Find a polynomial function whose graph has x-intercepts 3, 5, -4, and a y-intercept 180. Describe the features of its graph. Example 3: Write a polynomial function with real coefficients and zeros: 2, -5, and 3 + 4i.

  4. Assignment: page 408: 1 – 7, 8a, 11

More Related