UNIT 5 POLYNOMIAL FUNCTION LESSON 5 1 EXPLORING

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UNIT 5: POLYNOMIAL FUNCTION LESSON 5. 1: EXPLORING CUBIC FUNCTIONS

UNIT 5: POLYNOMIAL FUNCTION LESSON 5. 1: EXPLORING CUBIC FUNCTIONS

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ACT Practice Questions

ACT Practice Questions

Objectives Represent cubic functions using words, tables, equations and graphs. Interpret the key characteristics

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

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?

What is a Cubic Function?

Cubic Parent Function What is the parent function of 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

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?

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 is how many times a particular number is zero for a given polynomial

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

Transformation of Cubic Function

Cubic Function in Real World To find the volume of a cube use Linear.

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

Quadratic. Linear = cubic

Quadratic. Linear = cubic

Determining the Product of Linear Factors

Determining the Product of Linear Factors

Determining the Product of Quadratic an Linear Factors

Determining the Product of Quadratic an Linear Factors