I.  Graphs of Powers and Roots: Positive integers and negative integers. 

II. Solving Polynomial Equations.
III. Polynomial Roots in general.... How many?  

• Tools for Winplot used in this lab:

• Equation menu
• explicit
• Animation menu
  
• Families on Inventory.
• One
• zeroes
  

Set the parameters: N=2. A=1, B=0, C=0
I. Graphs of Powers and Roots

• Plot graphs with explicit for
  
• y = f(x) = x^N
• y = g1(x) = x^(1/N)
• y = g2(x) = root(N,x)
  
  
• Use animator N; family N.
• The power of the function f is N
• Note Asymptotes of f when N < 0
  

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II. Polynomial Identities. Solving Polynomial Equations.

• Verify graphically the identities:
  
• (x+A)^2 = x^2 + 2A*x + A^2
• (x-A)^2 = x^2 - 2A*x + A^2
• x^2  - A^2 = (x + A)*(x - A)
• Quadratic Equations
  
• y = Q1(x) = A*(x-B)^2 + C  
• Solve when Q1(x) = 0 using roots.
• y = Q2(x) = A*x^2 + Bx + C 
  
• Solve when Q2(x) = 0 using roots.

III. Polynomial Roots in general.... How many? Solving Polynomial Equations.

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