Reflection: Developing a Conceptual Understanding Intercepts of Polynomial Functions - Section 2: Section 2: Types of Zeros of Polynomial Equations


It is always more powerful to have student hypothesize about a concept before introducing it.  They begin to establish connections in their brain which increases their chance of retaining the information.  It also provides a certain amount of buy-in as the students are now invested in an idea or opinion.  This section provides a perfect place for that.  Students start with absolutely no idea how imaginary roots will look in a graph.  When I asked what they think would happen, I could tell that I got them thinking.  A few mentioned vertical translations like f(x)=x2+1 (Student Notes) but most were unsure.  Once I had them graph a few on their calculators, they were able to express that imaginary solutions created changes in direction in the curve that don't pass through the x-axis.   We then talked about how some imaginary solutions don't show up that way, but if you saw that kind of change in direction, that meant the presence of imaginary solutions.  

  Developing a Conceptual Understanding: Where is That Imaginary Solution
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Intercepts of Polynomial Functions

Unit 6: Polynomial Functions
Lesson 7 of 15

Objective: Students will be able to use key features of a polynomial graph to write the polynomial function.

Big Idea: The relationship between graphical and algebraic representations of polynomial functions, it all comes down to the roots!

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Math, polynomial functions, intercepts, Algebra 2, master teacher project
  51 minutes
image intercepts of polynomial functions
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