Do Now: Identify the zeros based on the graph. Indicate least possible degree. Create a polynomial with zeros of -1, 2, ½.

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Presentation transcript:

Do Now: Identify the zeros based on the graph. Indicate least possible degree. Create a polynomial with zeros of -1, 2, ½

Do Now: Create a polynomial with zeros of -1, 2, ½

Create a polynomial considering multiplicity Create a polynomial given a graph

Polynomial parent functions Standard form Follows same rules from chapter 2 (a, b, c, d, flip translations) Even FamilyOdd Family a>0 a 0a<0

Quick Sketch

Conjugate zeros theorem If a polynomial f(x) has a complex zero a + bi, then its conjugate a – bi is also a zero of f(x). Practice finding conjugates:

Create a polynomial Before: given zeros, convert to factors, find a, multiply Now: given graph, identify zeros, convert to factors, find a, multiply *Adding a step at the beginning

Consider Do Now problem:

Considering multiplicity Reminder: multiplicity refers to how many times a zero is occurring Even degree multiplicity causes a bounce ON the x-axis Odd degree multiplicity causes a wavy line THROUGH the x-axis We already have conceptual framework for this from chapter 2 with translated functions

Multiplicity If the graph bounces on the x-axis at a zero, the corresponding factor has an even multiplicity. If the graph crosses the x-axis, the corresponding factor has an odd multiplicity (could be 1)

Consider Do Now problem:

Creating Polynomials: Wrap Up Can create polynomials given zeros *Conjugate zeros theorem Can create polynomials given graph Find zeros by looking Conjugate Zeros Theorem

Sample Test Question Create a polynomial in standard from of least degree with zeros 4, 1-2i.

Homework We have not finished the section yet 1-8, even, even, 66, 68, 101