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Topic 11: Quadratic Equations and Functions (Ch. 10)

Goals and Problem Sets Handout
 

Goal 1:  Simplify radical expressions as far as possible (11-1; emphasis on problems that do not have variables)
Goal 2:  Tell whether a square root is rational or irrational  (11-1 and 10-3)
Goal 3: Approximate square roots with a calculator (10-3, handout)

Required tasks/resources Optional tasks/resources
Video: Radical Basics (32 min) Textbook pp.578 - 579 and 524 - 525
Problem set: Square Root Practice handout CoolMath Practice: Simplifying Radicals Cruncher
  Extension - Imaginary Numbers: http://mathforum.org/dr.math/faq/faq.imag.num.html and http://www.mathsisfun.com/numbers/imaginary-numbers.html
  Extension - Fractional exponents: http://www.mathsisfun.com/algebra/exponent-fractional.html

 

Goal 4:  Identify quadratic equations and functions; distinguish from linear and rational equations/functions (Most of chapter)
Goal 5:  Graph quadratic functions of the form y = ax2 + c without making a table (10 – 1)

Required tasks/resources  Optional tasks/resources
 Section DGI: Video: Graphing Quadratic Functions (33 min) with guided notes sheet Textbook pp. 510 - 513
 In-class activity: Graphing Quadratic Equations and Graphing Quadratic Equations by Hand Extension activity: "10-1 Extended Exploration" handout
Problem Set:  10 - 1 CoolMath Algebra Help: "Graphing Quadratics Lessons"
-->  Use "Intro" and Parts 1, 3, and 4 for our class; the others are extensions

 

Goal 6:  Recognize that the intersection of two graphs represents a solution of both of their equations simultaneously (10 – 4; see also 7 – 1)
Goal 7:  Solve quadratic equations using any of the following methods; choose an efficient method depending on the problem:
·    Solve quadratic equations by graphing and then locating solutions (10 – 4)
·    Solve quadratic equations by the square root method, aka "SADMEG" (10 – 4)

Required tasks/resources  Optional tasks/resources
 Class notes:  Solving by Graphing and Solving by the Square Root Method Textbook pp. 529 - 531
 Problem Set:  10 - 4 CoolMath Practice: Solving Quadratics by the Square Root

 
·    Solve quadratic equations by completing the square (10 – 6) 

Required tasks/resources  Optional tasks/resources
Video: Completing the Square (18 min) Textbook pp. 541 - 543
Class notes: Completing the Square Another video of Completing the Square
Video: Completing the Square Part 2 (17 min)  
Problem Set:  10 - 6  

 
·    Memorize the quadratic formula; solve quadratic equations by using the quadratic formula (10 – 7) 

Required tasks/resources  Optional tasks/resources

Memorize the Quadratic Formula

These Quadratic Formula Songs might help
(links may not work at school):

"Pop Goes the Weasel"

"Rolling in the Deep"

I'm not sure what song this is but it has examples

The Quadratic Formula Song

...and there are many more.  Seach and find...share your favorites with me!

 Textbook pp. 547 - 550
 Video: Using the Quadratic Formula (22 min) CoolMath Practice: The Quadratic Formula
 Problem Set:  10 - 7  
 

 
·    Solve quadratic equations by factoring (10 – 5)

Required tasks/resources  Optional tasks/resources
Video: Solving by Factoring (22 min) Textbook pp. 536 - 537
Problem Set:  10 - 5 CoolMath Explanation: Solving Quadratic Equations by Factoring
Help sheet: Comparing the Five Solution Methods CoolMath Practice: Solving Quadratics by Factoring
   

 

Goal 8: Find the discriminant of a quadratic function; use it to determine the number of solutions to the equation and the number of x-intercepts of the related function (10 – 8)

Required tasks/resources  Optional tasks/resources
Video: The Discriminant (21 min)  Textbook pp. 554 - 555
 Problem Set: 10 - 8  

  

Optional Extension: Graph quadratic functions of the form y = ax2 + bx + c by determining the y-intercept, x-intercepts, line of symmetry, and vertex (10 – 2)

 Tasks/resources
Textbook pp. 517 - 519
Problem Set 10 - 2

 

 Topic Summary

 Required tasks/resources

Problem Set: Chapter Test Assignment

 Optional tasks/resources