Unit 5: Polynomial Function Lesson 5.1: Exploring Cubic Functions This template can be used as a starter file for presenting training materials in a group setting. Sections Sections can help to organize your slides or facilitate collaboration between multiple authors. On the Home tab under Slides, click Section, and then click Add Section. Notes Use the Notes pane for delivery notes or to provide additional details for the audience. You can see these notes in Presenter View during your presentation. Keep in mind the font size (important for accessibility, visibility, videotaping, and online production) Coordinated colors Pay particular attention to the graphs, charts, and text boxes. Consider that attendees will print in black and white or grayscale. Run a test print to make sure your colors work when printed in pure black and white and grayscale. Graphics, tables, and graphs Keep it simple: If possible, use consistent, non-distracting styles and colors. Label all graphs and tables.

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ACT Practice Questions

Mastery is evidenced by scoring a 3 out of 4 on the Exit Slip Objectives Represent cubic functions using words, tables, equations and graphs. Interpret the key characteristics of the graph of cubic functions Analyze cubic functions in terms of their mathematical context and problem context Build cubic functions from linear and quadratic functions Mastery is evidenced by scoring a 3 out of 4 on the Exit Slip

Common Core Standards A.SSE.1: Seeing Structure in Expressions A.APR.1 Arithmetic with Polynomials and Rational Expressions F.IF.7: Interpreting Functions

What is a Cubic Function?

Cubic Parent Function What is the parent function of a cubic function?

Real Roots of Cubic Function Relative maximum: highest point in a particular section of a graph. Relative minimum: lowest point in a particular section of a graph.

Roots of Cubic Function How many x-intercepts does the function have ? How many zeros? Explain your reasoning. The function has only one x-intercept, (-2, 0) since it crosses the x-axis only once. The function has three zeros. The zero x = -2 is a multiple root, occurring 3 times.

Multiplicity Multiplicity is how many times a particular number is zero for a given polynomial function. The Fundamental Theorem of Algebra tells us that a cubic function must have 3 zeros. Roots may be any number including complex ones, and can even appear multiple times.

Transformation of Cubic Function

Cubic Function in Real World To find the volume of a cube use Linear . Linear . linear Volume is the amount of space that a substance or object occupies Remember, volume is 3D measure!

Quadratic . Linear = cubic

Determining the Product of Linear Factors

Determining the Product of Quadratic an Linear Factors