ALEX Resources

   View Standards     Standard(s): [MA2019] PRE-19 (9-12) 6 :

6. Analyze possible zeros for a polynomial function over the complex numbers by applying the Fundamental Theorem of Algebra, using a graph of the function, or factoring with algebraic identities.

[MA2019] PRE-19 (9-12) 26 :

26. Graph functions expressed symbolically and show key features of the graph, by hand and using technology. Use the equation of functions to identify key features in order to generate a graph.

a. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

b. Graph trigonometric functions and their inverses, showing period, midline, amplitude, and phase shift.

This informational material will explain how to identify the zeroes and intercepts of polynomial functions using graphs and equations. There are corresponding videos available. Practice questions with a PDF answer key are provided.  

   View Standards     Standard(s): [MA2019] PRE-19 (9-12) 6 :

6. Analyze possible zeros for a polynomial function over the complex numbers by applying the Fundamental Theorem of Algebra, using a graph of the function, or factoring with algebraic identities.

[MA2019] PRE-19 (9-12) 26 :

26. Graph functions expressed symbolically and show key features of the graph, by hand and using technology. Use the equation of functions to identify key features in order to generate a graph.

a. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

b. Graph trigonometric functions and their inverses, showing period, midline, amplitude, and phase shift.

This interactive will help students practice identifying zeroes and intercepts of polynomial functions using graphical representations. 

In this interactive, students will:

• • move the red line to see the intersections between the blue function and the red line.
    (The blue points are the places where the red line intersects the blue function.)
  • hover over the blue intercepts to see their coordinate values.

   View Standards     Standard(s): [MA2019] PRE-19 (9-12) 6 :

6. Analyze possible zeros for a polynomial function over the complex numbers by applying the Fundamental Theorem of Algebra, using a graph of the function, or factoring with algebraic identities.

This self-checking online assessment has 10 questions that will help students practice finding the zeroes and intercepts of polynomial functions. There are hints available on the screen, and there is an online scratchpad that students can use to work on the problems.

   View Standards     Standard(s): [MA2019] PRE-19 (9-12) 6 :

6. Analyze possible zeros for a polynomial function over the complex numbers by applying the Fundamental Theorem of Algebra, using a graph of the function, or factoring with algebraic identities.

This informational material will explain how to find all zeroes of a polynomial equation, including complex solutions. It will also introduce the concept of imaginary solutions. There is a corresponding video available. Practice questions with a PDF answer key are provided.  

   View Standards     Standard(s): [MA2019] PRE-19 (9-12) 6 :

6. Analyze possible zeros for a polynomial function over the complex numbers by applying the Fundamental Theorem of Algebra, using a graph of the function, or factoring with algebraic identities.

The Fundamental Theorem of Algebra tells us that any polynomial of degree n has n roots. At first, this may seem like a very convenient theorem but wait, what about counterexamples!? The function f(x) = x² + 1 clearly has no roots along the x-axis and we are told to believe that this function has 2. Does this mean that the Fundamental Theorem of Algebra is false?

In the interactive, students will:

• see two graphs on the complex plane.
  • The vertical axes are imaginary and the horizontal axes are real.
  • The vectors in the complex plane that compose the blue circle are mapped to the red circle in the complex plane through the function f(x) = x² + 1.
  • The vectors in the blue circle have been highlighted to see their mapping in the red circle.
• move the red point to see how the red circle maps to the complex plane.

   View Standards     Standard(s): [MA2019] PRE-19 (9-12) 6 :

6. Analyze possible zeros for a polynomial function over the complex numbers by applying the Fundamental Theorem of Algebra, using a graph of the function, or factoring with algebraic identities.

This self-checking online assessment has 10 questions that will help students analyze polynomial functions to find possible zeroes. There are hints available on the screen, and there is an online scratchpad that students can use to work the problems.