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Chapter 11 Quadratic Equations.

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Presentation on theme: "Chapter 11 Quadratic Equations."— Presentation transcript:

1 Chapter 11 Quadratic Equations

2 Sect. 11.1 Review of Solving Equations by Factoring
Ex. 1

3 Factoring Example continued

4 Sect. 11.2 Solving Quadratic Equations Using the Square Root Property
Ex. 1 Sect Solving Quadratic Equations Using the Square Root Property

5 Solving Quadratic Equations Using the Square Root Property cont

6 Solve an Equation of the Form (ax+b)2=k
Ex. 2 Solution set is {-1, 9}

7 Solve an Equation of the Form (ax+b)2=k Another Example

8 Use the Distance Formula
Ex. 4

9 Sect Complex Numbers

10 Find the Square Root of a Negative Number
Ex. 1

11 Multiply and Divide Square Roots Contining Negative Numbers
Ex. 2

12 Add and Subtract Complex Numbers

13 Multiply Complex Numbers

14 Multiply a Complex Number by Its Conjugate

15 Divide Complex Numbers

16 Ex. 7 Use the Square Root Property to Solve an Equation of the Form (ax+b)2 = k where k < 0

17 Sect. 11.4 Solving Quadratic Equations by Completing the Square
Ex. 1

18 Solving Quadratic Equations by Completing the Square continued

19 Complete the Square for an Expression of the form ax2 + bx, where b is an Odd Integer or a Fraction

20 Complete the Square for an Expression of the form ax2 + bx, where b is an Odd Integer or a Fraction continued

21 Solve an Equation of the Form ax2 + bx + c = 0 by Completing the Square
Ex. 3

22 Solve an Equation of the Form ax2 + bx + c = 0 by Completing the Square continued

23 Solve an Equation of the Form ax2 + bx + c = 0 by Completing the Square continued

24 Solve an Equation of the Form ax2 + bx + c = 0 by Completing the Square continued

25 Sect. 11.5 Solving Equations Using the Quadratic Formula

26 Examples of Solving Using the Quadratic Formula

27 Examples of Solving Using the Quadratic Formula continued

28 Examples of Solving Using the Quadratic Formula continued

29 Examples of Solving Using the Quadratic Formula continued

30 Determine the Number and Type of Solutions to a Quadratic Equation Using the Discriminant
Ex. 3

31 Determine the Number and Type of Solutions to a Quadratic Equation Using the Discriminant continued

32 Solve an Applied Problem Using the Quadratic Formula
Ex. 4 Solve an Applied Problem Using the Quadratic Formula

33 Solve an Applied Problem Using the Quadratic Formula continued

34 Solve an Applied Problem Using the Quadratic Formula continued

35 Ex. 1 Learn How to Decide Which Method to Use to Solve a Given Quadratic Equation

36 Learn How to Decide Which Method to Use to Solve a Given Quadratic Equation

37 Sect. 11.6 Equations in Quadratic Form
Solve an equation containing rational expressions.

38 Solve Quadratic Equations that Result from Equations Containing Radical Expressions

39 Solve an Equation in Quadratic Form By Factoring
Ex. 3 Solve an Equation in Quadratic Form By Factoring

40 Solve an Equation in Quadratic Form By Factoring

41 Ex. 4 Solve an Equation in Quadratic Form Using Substitution and then Factoring

42 Solve an Equation in Quadratic Form Using Substitution and the Quadratic Formula
Ex. 5

43 Use Substitution for a Binomial to Solve a Quadratic Equation
Ex. 6

44 Use Substitution for a Binomial to Solve a Quadratic Equation continued

45 Sect. 11.7 Formulas and Applications

46 More Examples of Solving for a Paricular Variable

47 Solve an Applied Problem Involving Volume
Ex. 3 Solve an Applied Problem Involving Volume

48 Solve an Applied Problem Involving Volume continued

49 Solve an Applied Problem Involving Area
Ex. 4

50 Solve an Applied Problem Involving Area cont

51 Solve an Applied Problem Modeled by a Given Quadratic Equation

52 Solve an Applied Problem Modeled by a Given Quadratic Equation continued


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