Intro W14

• 1. Current Page: Intro W14 (1 of 14)
  2. Resources W14 (2 of 14)
  3. TN W14, Assignment (3 of 14)
  4. 9.7 Video Lesson, Assignment (4 of 14)
  5. 9.7 Practice, Assignment (5 of 14)
  6. 9.8 Video Lesson, Assignment (6 of 14)
  7. 9.8 Practice, Assignment (7 of 14)
  8. Complex nrs Video Lesson, Assignment (8 of 14)
  9. Complex Numbers, Assignment (9 of 14)
  10. 7.6 Video Lesson, Assignment (10 of 14)
  11. 7.6 Practice, Assignment (11 of 14)
  12. 10.1 Video Lesson, Assignment (12 of 14)
  13. 10.1 Practice, Assignment (13 of 14)
  14. Outro W14 (14 of 14)

        Intro W14

  •  Objectives

  • The sections for this week are:
    • 9.7 Higher Roots
    • 9.8 Rational Exponents
    • 7.6 Quadratic Equations
    • 10.1 Solve Quadratic Equations Using the Square Root Property

   

   Intro and Learning Objectives (click on all tabs to see all sections)

  • • 9.7
    • 9.8
    • 7.6
    • 10.1

     Learning Outcomes

    In this section, you will:

    • Simplify expressions with higher roots
    • Use the Product Property to simplify expressions with higher roots
    • Use the Quotient Property to simplify expressions with higher roots
    • Add and subtract higher roots

     Intro

    Earlier in this chapter we defined the square root of a number.

    If \(n^2=m\) then n is a square root of m
    
    

    And we have used the notation $\sqrt{m}$ to denote the principal square root. 

    We will now extend the definition to higher roots.

    If $b^n=a$, then b is an nth root of a number a. 

    The principal nth root of a is written $\sqrt[n]{a}$.

          n is called the index of the radical.

     Learning Outcomes

    In this section, you will:

    • Simplify expressions with $a^{\frac{1}{n}}$
    • Simplify expressions with $a^{\frac{m}{n}}$
    • Use the Laws of Exponents to simply expressions with rational exponents

     Intro

    Rational exponents are another way of writing expressions with radicals. When we use rational exponents, we can apply the properties of exponents to simplify expressions. If $\sqrt[n]{a}$ is a real number and n≥2, $a^{\frac{1}{n}}=\sqrt[n]{a}$.

    In the same way $a^{\frac{m}{n}}=\sqrt[n]{a^m}$.

     Learning Outcomes

    In this section, you will:

    • Solve quadratic equations by using the Zero Product Property
    • Solve quadratic equations factoring
    • Solve applications modeled by quadratic equations

     Intro

    To solve quadratic equations we need methods different than the ones we used in solving linear equations. We will look at one method here and then several others in the next sections. We will first solve some quadratic equations by using the Zero Product Property. The Zero Product Property says that if the product of two quantities is zero, it must be that at least one of the quantities is zero. The only way to get a product equal to zero is to multiply by zero itself.

     Learning Outcomes

    In this section, you will:

    • Solve quadratic equations of the form $ax^2=k$ using the Square Root Property
    • Solve quadratic equations of the form $a\left(x-h\right)^2=k$ using the Square Root Property

     Intro

    Quadratic equations are equations of the form $ax^2+bx+c=0$, where a≠0. They differ from linear equations by including a term with the variable raised to the second power. We use different methods to solve quadratic equations than linear equations, because just adding, subtracting, multiplying, and dividing terms will not isolate the variable.

    We have seen that some quadratic equations can be solved by factoring. In this chapter, we will use three other methods to solve quadratic equations.

     Readings

    1. Text: Read the sections from Openstax book Links to an external site. (Links to an external site.)
    2. Videos: Watch all the videos from "Resources W14"

     Assignments

    • Take Notes Week 14         Due Friday night.
      

    Directions

    •  Each section is accompanied by a Handout. Each Handout contains a few definitions, a few "How To" explanations, examples, and "Try It" exercises. Using the structure of the handout you have to write your own notes. Your notes must contain:

    • • Your name
      • The name of the section
      • Definitions and "How To" from the provided handout (this is optional, however, it will be a good idea to have the complete notes)
      • Everywhere there is a "Read Ex nr..." you have to read the example from the ebook and write in your notes : "I read the Ex nr..." . The link for the section in the ebook is provided at the bottom of the page.
      • You have to solve ALL "Try It" exercises.

    After you complete your notes you have to submit them. See Take Notes Methods. 

     

    • Video quizzes Week 14          Due Saturday night 11:59pm.

    Directions

    • To learn the material for this sections, take notes while watching each video and then demonstrate what you learned by doing the exercise below it.

     

    • Homework Week  14              Due Sunday night 11:59pm.
    •  

    Directions

    • There are 5 Practice  Homework this week. This are online Homework but you do not have to leave Canvas. Just click on each link, answer the questions, and came back for the next section. There is no partial credit, each question is either 100% good or not. However you have unlimited attempts for each question. A 5% per day penalty applies for Late work if you'll do it until Tuesday night. After that the Homework will be open only for practice.

     

  The due dates for assignments are Friday, Saturday, and Sunday.

  However, you can submit them until Tuesday night next week.

  A 5% per day penalty applies for late work if you'll do it until Tuesday night.