Follow the link below for more instruction and practice solving inequalities using graphs.

How to Solve a Quadratic Inequality

For additional practice, do the following:

  1. 2x2 − 5x − 3 < 0
  2. -x2 + x = 20 ≥ 0
  3. x2 − 12x + 36 ≤ 0
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Check Your Answer

- 1 2 < x < 3 Close Pop Up

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-4 ≤ x ≤ 5Close Pop Up

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x = 6Close Pop Up

Next, in your journal, write a description or sketch an example of the graph of quadratic inequalities that have the following number(s) of solutions:

  1. One solution
  2. No solutions
  3. Infinite solutions
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Check Your Answer

The graph just touches the axis or y-value below or above which the inequality is true. One point satisfies the inequality (the vertex)Close Pop Up

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The graph falls completely above or below the y-value given in the inequality-there is nothing to shadeClose Pop Up

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The graph overlaps the area of y-values by rising above or dipping below and includes an infinite number of points.Close Pop Up