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EXAMPLE 4

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.

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EXAMPLE 4

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  1. 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.

  2. –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

  3. 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.

  4. 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

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