1 / 16

Chapter 9

Chapter 9. Section 1. Solving Quadratic Equations by the Square Root Property. Review the zero-factor property. Solve equations of the form x 2 = k , where k > 0. Solve equations of the form ( ax + b ) 2 = k , where k > 0. Use formulas involving squared variables. 9.1. 2. 3. 4.

lucas-craig
Télécharger la présentation

Chapter 9

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 9 Section 1

  2. Solving Quadratic Equations by the Square Root Property Review the zero-factor property. Solve equations of the form x2 = k, where k > 0. Solve equations of the form (ax + b)2 = k, where k > 0. Use formulas involving squared variables. 9.1 2 3 4

  3. In Section 6.5, we solved quadratic equations by factoring. Since not all quadratic equations can easily be solved by factoring, we must develop other methods. Solving Quadratic Equations by the Square Root Property Slide 9.1-3

  4. Objective 1 Review the zero-factor property. Slide 9.1-4

  5. Solving Quadratic Equations by the Square Root Property Recall that a quadratic equation is an equation that can be written in the form for real numbers a, b, and c, with a≠0. We can solve the quadratic equation x2 + 4x + 3 = 0 by factoring, using the zero-factor property. Standard Form Zero-Factor Property If a and b are real number and if ab = 0, then a = 0 or b = 0. Slide 9.1-5

  6. EXAMPLE 1 Solving Quadratic Equations by the Zero-Factor Property Solution: Solve each equation by the zero-factor property. 2x2−3x + 1 = 0 x2 = 25 Slide 9.1-6

  7. Objective 2 Solve equations of the form x2 = k, where k >0. Slide 9.1-7

  8. Square Root Property If k is a positive number and if x2 = k, then or The solution set is which can be written (± is read “positive or negative” or “plus or minus.”) When we solve an equation, we must find all values of the variable that satisfy the equation. Therefore, we want both the positive and negative square roots of k. Solve equations of the form x2 = k, where k> 0. We might also have solved x2 = 9 by noticing that x must be a number whose square is 9. Thus, or This can be generalized as the square root property. Slide 9.1-8

  9. Solve each equation. Write radicals in simplified form. EXAMPLE 2 Solving Quadratic Equations of the Form x2 = k Solution: Slide 9.1-9

  10. Objective 3 Solve equations of the form (ax + b)2 = k, where k >0. Slide 9.1-10

  11. Solve equations of the form (ax + b)2 = k, where k> 0. In each equation in Example 2, the exponent 2 appeared with a single variable as its base. We can extend the square root property to solve equations in which the base is a binomial. Slide 9.1-11

  12. Solve (p– 4)2 = 3. EXAMPLE 3 Solving Quadratic Equations of the Form (x + b)2 = k Solution: Slide 9.1-12

  13. Solve (5m + 1)2 = 7. EXAMPLE 4 Solving a Quadratic Equation of the Form (ax + b)2 = k Solution: Slide 9.1-13

  14. Solve (7z + 1)2 = –1. EXAMPLE 5 Recognizing a Quadratic Equation with No Real Solutions Solution: Slide 9.1-14

  15. Objective 4 Use formulas involving squared variables. Slide 9.1-15

  16. Use the formula, to approximate the length of a bass weighing 2.80 lb and having girth 11 in. EXAMPLE 6 Finding the Length of a Bass Solution : The length of the bass is approximately 17.48 in. Slide 9.1-16

More Related