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In this course you will discover how to solve quadratic functions and equations using algebraic processes. We will begin by applying the square root method and then move into solving by factoring, completing the square, and quadratic formula. These processes will become very important to understand how to determine solutions of a quadratic as well as reason real world applications. The course will start with identifying essential questions that will provide a theme of what you are expected to learn throughout the course. We will then discover the essential definitions and processes that will be necessary to complete this course.
You will then have the opportunity to try on your own over 100 example problems for each process so that you can master the skills set out in this course. If at anytime you want to check your answer or get stuck. Each problem is accompianed with a step by step tutorial video to help you along.
After you have completed the work you can answer the essential questions at the end of this course or work on the challenge problems to round off your learning and prepare you for the next level.
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Section 1: Introduction  

Lecture 1  02:33  
In this video I will go over what is needed in this course for you to learn how to algebraically solve a quadratic equation and function. There are many processes that we will use in this course and it is important that you have the fundamentals before you start. 

Section 2: Basics for solving quadratic equations with factoring  
Lecture 2  02:36  
A quadratic can be a monomial, binomial or trinomial where the the highest degree is two. For example x^2,3x^25, 2x^2+3x, and (1/2)x^2 +4x2 are all examples of quadratics. The two different examples we will discover are an quadratic equation and function. The only difference between then two within the context of how we will use them is their output variables. 

Lecture 3  08:01  
Factoring is the process of rewriting an expression as a product of it's factors. We start by learning how to determine the factors of a number. For instance the factors of 12 are 12,6,4,3,2,1 because they evenly divide into 12. If we were going to write 12 as a product of it's factors one example would be 6*2. This is our goal for factoring expressions with variables as well. We can always check our answer by multiplying the factors together. Factoring is important because it allows us to transform an expression where we can apply the zero product property for solving and simplify the expression when needed. 

Lecture 4  06:30  
When factoring out a GCF from an expression we need to know what a GCF really means. "GCF" mean greatest common factor. So what we are looking for is a common factor meaning a number or term that evenly divides into each term. When we say factor out we really mean divide out but rewrite the expression as a product. 

Lecture 5  03:43  
Solving a quadratic means finding the values of x or your input variable when your output variable (y) is zero. This is the same for functions. When the output variable is zero then our point lies on the xaxis of the graph so when we think of the graphical solution it is the xintercepts of the quadratic. 

Lecture 6  04:32  
The zero product property is essential to solving quadratics by factoring. What the zero product simply states is that if you have the product of two terms or expressions that equal zero then one of those solutions has to equal zero. Therefore to find the value of each term or expression we set them equal to zero and solve. 

Section 3: Solving Quadratic Equations by factoring  
Lecture 7 
Overview for how to solve a quadratic by factoring out the GCF

05:23  
Lecture 8 
Examples for solving a quadratic by factoring out the GCF

07:27  
Lecture 9 
Quiz  Solving a quadratic by factoring out the GCF

Article  
Lecture 10  02:00  
There are a couple of ways to factor a quadratic when a=1. Throughout this course I will talk about a couple of them. While the goal is to eventually factor in your head. At times there will be problems that are hard to factor or not even possible. Therefore we will use a couple of techniques to ensure our answer is correct. 

Lecture 11 
Examples for solving a quadratic when a is 1

14:12  
Lecture 12 
Quiz  Solving by factoring when a is 1

Article  
Lecture 13  06:48  
There are multiple ways to solve a quadratic when a is not equal to one. In this video we will discuss how to do that mentally as well as two other approaches where you can break down the problem to ensure your answer is correct and it can be factored. 

Lecture 14 
Examples for solving a quadratic when a is not 1

18:22  
Lecture 15 
Quiz  Solving a quadratic when a is not 1

Article  
Lecture 16  02:43  
To solve a quadratic by applying the difference of two squares it is very important that we have our quadratic set equal to zero. We will then apply the factoring technique of the difference of two squares and use the zero product property to solve. 

Lecture 17 
Quiz  Solving a quadratic by using the difference of two squares

Article  
Lecture 18  02:27  
Process for solving by factoring a perfect square trinomial: 1.) Set your equation equal to zero 2.) Factor GCF if necessary to obtain square terms 3.) Determine if your coefficient and constant are square numbers and can be written as factors by taking the square root. 4.) Write your perfect square as a binomial squared to solve using the square root method or write as the product of two binomials and solve using the zero product property. 

Lecture 19 
Quiz  Solving a quadratic as a perfect square trinomial

Article  
Lecture 20 
Examples for solving a quadratic using special factoring techniques

06:19  
Section 4: Basics for solving Quadratic Equations without factoring  
Lecture 21 
What is the quadratic formula?

01:45  
Lecture 22 
What are the different types of solutions to a quadratic?

01:53  
Section 5: Solving Quadratic Equations without factoring  
Lecture 23  03:33  
Process for solving by square root method:


Lecture 24  10:19  
Need to create 

Lecture 25  04:40  
Here are the general steps for solving a quadratic by completing the square 1.) Set your equation equal to zero 2.) Factor if necessary out of your quadratic and linear terms so a=1 3.) (b/2)^2 then add to your binomial to make it a trinomial and add to the other side of the equation. 4.) Factor your perfect square trinomial to a binomial squared. 5.) Apply inverse operations by adding or subtracting on both sides to eliminate your c 6.) Take the square root on both sides to eliminate the square 7.) Add or subtract your factor to isolate your variable 

Lecture 26 
Examples for solving a quadratic by completing the square

12:06  
Lecture 27 
Quiz  Solving quadratics by completing the square

Article  
Lecture 28  04:08  
To solve a quadratic we will want to understand the discriminant and determine it's value. This will one help us solve using the quadratic formula but also give us an idea of the roots of the equation. The discriminant is b^24ac which is under the square root in the quadratic formula. After we have determined it's value and noted the number of roots we can simplify the remaining equation to solve for x. 

Lecture 29 
Examples for solving a quadratic using the quadratic formula

11:01  
Lecture 30 
Examples for solving a quadratic using the quadratic formula; complex solutions

12:24  
Lecture 31 
Quiz  Solving a quadratic using the quadratic formula

Article  
Section 6: Writing the equation of a parabola  
Lecture 32 
Examples for completing the square to convert from standard to vertex form

19:03  
Lecture 33 
Quiz  Writing the equation of the parabola from standard form to vertex form

Article  
Lecture 34 
Examples for writing the patabola of a quadratic given vertex through a point

09:06  
Lecture 35 
Quiz  Writing the equation of a parabola given the vertex and a point

Article  
Lecture 36 
Examples for writing the equation of a parabola given three points

10:39  
Lecture 37 
Quiz  Writing the equation of a parabola given three points

Article  
Section 7: Basics for graphing quadratics  
Lecture 38 
What is standard form of a quadratic

02:48  
Lecture 39 
What is vertex form of a quadratic

01:44  
Lecture 40 
What is the vertex?

05:03  
Lecture 41 
What is the axis of symmetry?

04:28  
Lecture 42 
What is the max and min of a quadratic?

04:28  
Lecture 43 
What is the line of symmetry of a quadratic?

03:04  
Section 8: Graphing Quadratic Equations  
Lecture 44 
How to find the vertex of a quadratic in standard form

02:57  
Lecture 45 
Examples for graphing a quadratic using the axis of symmetry and vertex

19:39  
Lecture 46 
Examples for graphing a quadratic by converting from standard form to vertex

17:46  
Lecture 47 
Examples for identifying the vertex, domain and range in vertex form

13:15  
Lecture 48 
Graphing a quadratic in vertex form using transformations

15:04  
Lecture 49 
Quiz  Graphing a Quadratic in standard form

Article  
Section 9: BONUS  Basics for Complex Numbers  
Lecture 50 
What is a complex number?

02:08  
Lecture 51 
What is an imaginary number?

01:55  
Lecture 52 
What is the imaginary unit i

01:55  
Section 10: BONUS  Complex Numbers  
Lecture 53 
Overview for how we add and subtract complex numbers

03:04  
Lecture 54 
Examples for adding and subtracting complex numbers

05:10  
Lecture 55 
Quiz Adding and Subtracting Complex Numbers

Article  
Lecture 56 
Overview for how we multiple complex numbers

02:27  
Lecture 57 
Examples for multiplying complex numbers

09:42  
Lecture 58 
Quiz Multiply Complex Numbers

Article  
Lecture 59 
Simplifying expressions with complex numbers using multiple operations

10:21  
Lecture 60 
Simplify Expression with multiple operations

Article  
Lecture 61 
Examples for writing an expression using complex numbers the simplifying

04:45  
Lecture 62 
Quiz Simplify expression using the imaginary unit i

Article  
Lecture 63 
Overview for how we divide complex numbers

03:56  
Lecture 64 
Examples for dividing complex numbers

11:13  
Lecture 65 
Quiz Dividing complex numbers

Article  
Lecture 66 
Simplifying complex numbers to a higher power

09:16  
Lecture 67 
Quiz Simplifying Complex Numbers to a higher power

Article  
Lecture 68 
Graph

Article 
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