Quadratic Functions

 
Topic
 
 
Mastery Objective

Students will be able to...
 
Video
 
Survey
 
Khan Academy
Practice

 
 
Classwork/
Answer Keys

  Quadratic Modeling...

              Using Matrices 
 
        
              Using Differences

 
determine if a quadratic function can model a set of points or a sequences of numbers.

write a quadratic equation to model a set of values when appropriate using a system of equations.

write a quadratic equation to model a set of values when appropriate using an "off-by" table.
 





 










 





Vertex Form of
Quadratic Functions

 
write the equation of a parabola in vertex form from its graph.

graph a parabola given a quadratic function in vertex form.
 
 
                






 
 

 
 
https://dl.dropboxusercontent.com/u/12153667/Vertex%20Form%20CW.pdf

 


Completing the Square



change a quadratic function written in standard form into vertex form by "completing the square."







 



 
a=1

a ≠ 1
 
              

 


Standard Form of
Quadratic Functions




graph a parabola given a quadratic function in standard form. 

rewrite the standard form of a quadratic function in vertex form.
 







Questions Only


Standard Form

Vertex & 
Standard Form
 


                     

 
Review for Quiz

 

  https://sites.google.com/site/algebra2honorsfhs/_/rsrc/1342149947648/notes-on-video/chapter-5/pdf_icon.pnghttps://sites.google.com/site/algebra2honorsfhs/_/rsrc/1342149947648/notes-on-video/chapter-5/pdf_icon.png

   Factoring Quadratic Expressions 

Exploration



An Introduction 



An Alternative Method for Factoring Non-Monic Quadratics




Special Examples*













factor any quadratic expression.







               https://www.youtube.com/watch?v=KaUoCZxNz5I



 


1-Variable

2-Variable 
 





Factored Form of 

Quadratic Functions 


write the equation of a parabola in factored form from its graph.

graph a parabola given a quadratic function in factored form. 



  
 


  


 
     Complex Numbers

            Introduction


            Graphing




            Adding/Subtracting



            Multiplying & Dividing


classify numbers in the following categories: complex, real, imaginary, rational, irrational, integers, whole numbers and natural numbers.


indicate where complex numbers are on the number plane and determine their absolute value.



calculate powers of i.



add, subtract, multipy and divide complex numbers. 


recognize that multiplying a number by i, rotates the number on the number plane 90 degrees counterclockwise.



                

     
            





 














 
add/subtract

multiplying

dividing

 
abs value





            





 
The Quadratic Formula



derive the quadratic formula.

calculate the discriminant of a quadratic equation to determine the type of roots it has.

use the quadratic formula to solve for the roots to a quadratic equation.

 

Homework Worksheet

  

 


Quadratic Applications
 

write the equation for an object's height as a function of time based on the projectile motion formula.

optimize a given variable provided that it can be modeled with a quadratic expression.


                 

 
 


 




Solving Quadratic Equations

 

solve for the roots of any quadratic equation using one of the following methods: completing the square, using the quadratic formula, factoring, or graphing.
 




 



 
a=1

≠ 1
 



 
Review for Test