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Exploring Polynomial Functions: Finding Roots and Writing Equations

In today's Algebra II Honors class, we focus on understanding polynomial functions and the number of possible zeros—positive, negative, and imaginary—using Descartes’ Rule of Signs. We'll explore how to identify roots of polynomial equations, determine their equations, and understand their graphs. Additionally, we'll practice writing polynomial equations based on given roots, including the usage of complex conjugates. Don't forget about the group quiz tomorrow on the new material! Make sure to review the Rational Zero Theorem and complete your assigned practice problems.

gary-davidson
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Exploring Polynomial Functions: Finding Roots and Writing Equations

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Presentation Transcript

  1. Algebra II Honors—Day 47

  2. Warmup • Tell the number of possible positive, negative, and imaginary zeros for the following function:

  3. Goals for today • Reminders: • Group quiz tomorrow—on new material through Descartes’ Rule of Signs • Essential Question/New Material

  4. Essential Question • How do I find the roots of a polynomial function? • How do I determine an equation and graph of a polynomial function given its roots?

  5. Rational Zero Theorem • Use Descartes’ Rule of Signs to identify the number of possible positive and negative zeros. • Use handout for notes and examples on the Rational Zero Theorem.

  6. Writing equations from roots • When you know ALL the roots of an equation, write the FACTORS and multiply them together. • EXAMPLE: Given these roots, write the equation • Use the roots to write the factors and multiply them.

  7. More Practice—Write equations Why?? Roots: Factors: Equation:

  8. More Practice—Write equations Multiply the complex conjugates first to get rid of the imaginary number Roots: Factors: Equation:

  9. More Practice—Write equations Roots: Factors: Equation: NEXT SCREEN!!!

  10. More Practice—Write equations Multiply the two factors with imaginary numbers to get a difference of squares. Equation:

  11. Homework • Handout • P. 405—even only • P. 406—#1, 3

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