Unit 9

Quadratic Functions and Equations

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Functions
Essential Question: What are the characteristics of Quadratic Functions?

Solving Equations and Inequalities
Essential Question: How can you SOLVE a quadratic equation?

Modeling
Essential Question: How can you use functions to model real-world situations?
   

 

Desmos.com Graphing Calculator

Shodor Graphing Calculators

Lesson/Objective Supplemental Lessons On-line Practice Suggested
Homework
9-1  Quadratic Graphs and Their Properties

Objective:  To graph quadratic functions of the form y=ax2 and y=ax2+c.

Essential Understandings: 
The family of quadratic functions models certain situations where the rate of change is NOT CONSTANT. These functions are are graphed by a symmetric curve  with a highest of lowest point corresponding to a maximum or minimum value.
 


Video Tutors

Graphing a quadratic function using a table, y = ax2

Graphing a quadratic function using a table, y = ax2 + c

Using a quadratic function to model the height of an object - Example 1 


self-check quiz

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Additional
PROBLEMS

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You can use a graphing calculator to support your work
You should be able to answer many of these questions without generating a specific graph,
for example #34-39 & #44-47 should be "at-a-glance" answers

BOTH #9-1 & #9-2 DUE ON THE SAME DAY!!

hw #9-1: Due

pg 549-551, #5-10 All, 11-23 Odd, 34-36 (you should be able to answer these just from what you know about parabolas and their graphs), 41

hw #9-2: Due 

pg 556-557 #5,6, 7-15 Odd, 16-19 All, 21-27 Odd

 

 

9-2  Quadratic Functions

Objective:  To graph quadratic functions of the form y=ax2+bx+c.

Essential Understandings: 
In the quadratic function y=ax2+bx+c, the value of b translates to the position of the axis of symmetry.
 


Video Tutors

Graphing a quadratic function, y = ax2 + bx + c

Using a quadratic function to model the height of an object - Example 2

Graphing a quadratic inequality


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9-3  Solving Quadratic Equations

Objective:  To solve quadratic equations by graphing and using square roots

Essential Understandings: 
Quadratic equations can be solved in a variety of methods, including graphing and using square roots.

 


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Solving quadratic equations by graphing

Solving quadratic equations using square roots

 


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BOTH #9-3 & #9-4 DUE ON THE SAME DAY!!

hw#9-3: Due 

pg 563-565 #1-7 All, #9, 13,17,21,25,29.33

hw#9-4: Due

pg 570-572 #1-7 9 ,11, 13, 15, 21, 25

 

9-4  Factoring to Solve Quadratic Equations

Objective: To solve quadratic equations by factoring and using the zero-product property

Essential Understandings: 
Quadratic equations can be solved in a variety of methods, including factoring and using the zero-product property.
 

Video Tutors

Solving quadratic equations by factoring


VIDEO LESSON

Worked Examples:
Example 1
Exmaple 2
Example 3
 


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QUIZ on sections 9-1 thru 9-4
TBA

9-5  Completing the Square

Objective: To solve quadratic equations by completing the square

Essential Understandings: 
When a quadratic equation cannot be solved by factoring, COMPLETING THE SQUARE is a method that will work for ANY quadratic equation. 

REAL ALGEBRA-TICIANS COMPLETE THE SQUARE!!!
 


Video Tutors

Solving quadratic equations using completing the square

Solving quadratic equations using completing the square when a does not equal 1


VIDEO LESSON

Worked Examples:
Completing the Square 1

Completing the Square 2


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hw#9-5: Due 

pg 579 #1-6,7-17 Odd


9-6  The Quadratic Formula and the Discriminant

Objective: To solve quadratic equations using the QUADRATIC FORMULA

Essential Understandings: 
When a quadratic equation cannot be solved by factoring and COMPLETING THE SQUARE seems difficult (code for: "you are a weenie") the QUADRATIC FORMULA is a method that will work for ANY quadratic equation.

 

Better Way - by Ben Harper


Video Tutors

Solving quadratic equations using the quadratic formula

Solving real-world problems using the quadratic formula

Using the Discriminant to find the number of solutions and solve problems

Choosing the appropriate method to solve quadratic equations


VIDEO LESSON

Quadratic Formula Proof
 


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hw#9-6: Due 

pg 586-587
#11-21 Odd 23-27 All


 

UNIT TEST REVIEW   UNIT 9 EXTRA PRACTICE

CUMULATIVE REVIEW 1-9

hw#9-7: Due 

BE SURE TO READ (a novel concept) Problem 3 on pg 585.

pg 587 #29-40 ALL

Unit 9 Problem Set A

A SMART STUDENT would begin to look at pages 603-605... the UNIT 9 TEST will be on Sections 9-1 thru 9-6 ONLY.

If you try the Chapter Test on pg 607 IGNORE questions #19-22

[PS 9A Answers]

 
UNIT 9 TEST:
Sections 9-1 thru 9-6 ONLY
TBA
SKIP sections 9-7 & 9-8
(left iu place BELOW just in case you can't resist!!)
9-7  Linear, Quadratic, and Exponential Models

Objective: To choose a linear, quadratic, or exponential model for data.

Essential Understandings: 
A good understanding the various types of algebraic functions is useful so that mathematical models can be applied to real-world data in an appropriate manner. 
 

Video Tutors

Modeling data using a linear, quadratic, or exponential model - Example 1

Modeling data using a linear, quadratic, or exponential model - Example 2

Khan Vertex Form Example

 


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hw#9-7: Due 
pg
9-8  Systems of Linear and Quadratic Equations

Objective: To solve systems of linear and quadratic equations.

Essential Understandings: 
Systems of linear and quadratic equations can be solved graphically and algebraically. This type of system can have two solutions, one solution, or no solutions.

 

Video Tutors


 


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hw#9-8: Due 
pg