1 / 17

5.7 : Graphing and Solving Quadratic Inequalities

5.7 : Graphing and Solving Quadratic Inequalities. Objectives: Students will be able to… Graph quadratic inequalities in 2 variables Solve quadratic inequalities in 1 variable. Quadratic Inequalities in 2 variables…. The graph contains all solutions ( x,y ) that make the inequality true.

tiva
Download Presentation

5.7 : Graphing and Solving Quadratic Inequalities

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. 5.7 : Graphing and Solving Quadratic Inequalities Objectives: Students will be able to… Graph quadratic inequalities in 2 variables Solve quadratic inequalities in 1 variable

  2. Quadratic Inequalities in 2 variables… The graph contains all solutions (x,y) that make the inequality true

  3. Graphing a Quadratic Inequality in 2 variables: • Graph the parabola with the equation y=ax2 + bx +c (dashed for > or < ; solid line for > or <) • Choose a point (x,y) inside the parabola and check whether the point is a solution of the inequality • If the point is a solution, shade the region inside the parabola. If it is not a solution, shade the region outside the parabola.

  4. Example Graph y < 2x2 – 5x -3

  5. Graph y > - x2 +5

  6. Graph y>x2 – 4x +3

  7. Systems of Quadratic Inequalities • Graph each inequality one at a time on the same coordinate plane • Where the shading overlaps is your solution region. Darken this area.

  8. Example: y < - x2 + 9 y > x2 +5x -6

  9. Example: y < - 3x2 y > (-1/2)x2 - 5

  10. Quadratic Inequalities in 1 variable ax2 + bx + c > 0 ( or >) ax2 + bx + c < 0 ( or <) • Two ways to solve: • Graphically • Algebraically

  11. How to solve graphically • Graph y = ax2 + bx +c (make sure to set=0 first) • Be sure to identify the x – intercepts (may need to use Quadratic Formula…uh oh!!) • If ax2 + bx + c < 0 ( or <), you are looking for the x values where the graph is belowthe x axis. ( or on or below) • If ax2 + bx + c > 0 ( or >), you are looking for the x values where the graph is above the x axis. ( or on or above)

  12. Solve by graphing: x2 – 5x + 6 > 0 • Where is your graph above the x-axis?

  13. Solve by graphing: x2 – 11x + 5 < 0 • Where is your graph below the x – axis?

  14. Solving 1 variable inequalities algebraically Solve 2x2 – x > 3 • Write the corresponding equation: 2x2 – x = 3 2. Solve the equation: 3. Test these critical x values on a number line. Pick x values to the left and right of the critical values to see what numbers satisfy the inequality:

  15. Solve algebraically. 1. 2x2< 8 2. x2 – 10x + 24 > 0

  16. Ticket out: Solve 16 – x2> 0

  17. Remember this material when you are finding domain and range in precalculus and calculus!!!!

More Related