1 / 9

4.9 Solving Quadratic Inequalities

4.9 Solving Quadratic Inequalities. ANSWER. The solution of the inequality is –3 ≤ x ≤ 2. Solve a quadratic inequality using a table. EXAMPLE 4. Solve x 2 + x ≤ 6 using a table. SOLUTION. Rewrite the inequality as x 2 + x – 6 ≤ 0 . Then make a table of values.

tiger
Download Presentation

4.9 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. 4.9 Solving Quadratic Inequalities

  2. ANSWER The solution of the inequality is –3 ≤ x ≤ 2. Solve a quadratic inequality using a table EXAMPLE 4 Solve x2 + x ≤ 6 using a table. SOLUTION Rewrite the inequality as x2 + x – 6 ≤ 0. Then make a table of values. Notice that x2 + x – 6 ≤ 0 when the values of xare between –3 and 2, inclusive.

  3. –1+ 12– 4(2)(–4) x = –1+33 2(2) x = 4 x 1.19 orx –1.69 Solve a quadratic inequality by graphing EXAMPLE 5 Solve 2x2 + x – 4 ≥ 0 by graphing. SOLUTION The solution consists of the x-values for which the graph of y = 2x2 + x – 4 lies on or above the x-axis. Find the graph’s x-intercepts by letting y = 0 and using the quadratic formula to solve for x. 0 = 2x2 + x – 4

  4. Solve a quadratic inequality by graphing EXAMPLE 5 Sketch a parabola that opens up and has 1.19 and –1.69 as x-intercepts. The graph lies on or above the x-axis to the left of (and including) x = –1.69 and to the right of (and including) x = 1.19. ANSWER The solution of the inequality is approximately x ≤ –1.69 or x ≥ 1.19.

  5. for Examples 4 and 5 GUIDED PRACTICE Solve the inequality 2x2 + 2x ≤ 3using a table and using a graph. ANSWER –1.8 ≤ x ≤ 0.82

  6. Solving a quadratic inequality algebraically -9 -6 0 -8 -4

  7. EXAMPLE 7 Solve a quadratic inequality algebraically Solve x2 – 2x > 15 algebraically. SOLUTION First, write and solve the equation obtained by replacing > with = . x2 – 2x = 15 Write equation that corresponds to original inequality. x2 – 2x – 15 = 0 Write in standard form. (x + 3)(x – 5) = 0 Factor. x = –3 orx = 5 Zero product property

  8. (–4)2– 2(–4) = 24 > 15 62 –2(6) = 24 >15 12 – 2(1)= –1 >15   ANSWER The solution is x < –3 orx > 5. EXAMPLE 7 Solve a quadratic inequality algebraically The numbers –3 and 5 are the critical x-values of the inequality x2 – 2x > 15. Plot –3 and 5 on a number line, using open dots because the values do not satisfy the inequality. The critical x-values partition the number line into three intervals. Test an x-value in each interval to see if it satisfies the inequality. Test x = – 4: Test x = 1: Test x = 6:

  9. Solve the inequality using any method.

More Related