1 / 18

Chapter 2

Chapter 2. 2-7 Solving quadratic inequalities. Objectives. Solve quadratic inequalities by using tables and graphs. Solve quadratic inequalities by using algebra. Solving quadratic inequalities.

janina
Download Presentation

Chapter 2

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 2 2-7 Solving quadratic inequalities

  2. Objectives Solve quadratic inequalities by using tables and graphs. Solve quadratic inequalities by using algebra.

  3. Solving quadratic inequalities Many business profits can be modeled by quadratic functions. To ensure that the profit is above a certain level, financial planners may need to graph and solve quadratic inequalities. A quadratic inequality in two variables can be written in one of the following forms, where a, b, and c are real numbers and a ≠ 0. Its solution set is a set of ordered pairs (x, y).

  4. Solving quadratic inequalities A quadratic inequality in two variables can be written in one of the following forms, where a, b, and c are real numbers and a ≠ 0. Its solution set is a set of ordered pairs (x, y). y < ax2 + bx + c y > ax2 + bx + c y ≤ ax2 + bx + c y ≥ ax2 + bx + c

  5. Solving inequalties

  6. Example#1 Graphing Quadratic Inequalities in Two Variables Graph y ≥ x2 – 7x + 10. Step 1 Graph the boundary of the related parabola y = 2x2 – 5x – 2 with a solid curve. Its y-intercept is –2, its vertex is (1.3, –5.1), and its x-intercepts are –0.4 and 2.9.

  7. Example#1 continue Step 2 Shade above the parabola because the solution consists of y-values greater than those on the parabola for corresponding x-values.

  8. Example#2 Graph each inequality. y < –3x2 – 6x – 7

  9. Example#3 Solve the inequality by using tables or graphs. x2 + 8x + 20 ≥ 5

  10. Example#4 Solve the inequality x2 – 10x + 18 ≤ –3 by using algebra.

  11. Example#5 Solve the inequality by using algebra. x2 – 6x + 10 ≥ 2

  12. Example#6 Solve the inequality by using algebra. –2x2 + 3x + 7 < 2

  13. Student guided practice Let’s work on graphing quadratic inequalities worksheet problems 1-5 Do problems 24-26 on book page 115

  14. Homework Do evens problems from 35-46 from the book page 115.

  15. Closure Today we learn how to solve quadratic inequalities by graphing and by solving algebraically Next class we are going to continue with 2-9 operations with complex numbers/

  16. Have a nice day!!!!

More Related