How to Solve Second-Degree Inequalities

Inequality equations are equations where the two sides are not equal. Instead of an equal sign, either a greater-than sign, ">," or a less-than sign, "<," indicates the relationship between the two sides. A second-degree inequality equation has at least one x or y variable with a power greater than one, such as x to the second power. These equations are best solved by plotting the equation and getting a visual representation of the solution.

Instructions

    • 1

      Find and write down the second-degree equation in question. As an example:

      y > 2x^2 + 3x + 4

    • 2

      Convert the inequality sign into an equal sign. Continuing with our example:

      y = 2x^2 + 3x + 4

    • 3

      Plot the equation in Step 2. Continuing with the example, draw an x-y graph labeling both the x and y axis. Ensure the graph extends in the positive and negative direction for both the x and y axis. Start at x = 0. At x = 0, y is 4. Plot the point (0, 4) on the graph. At x = 1, y is 9. Plot the point (1, 9) on the graph. At x = 2, y is 18. Plot the point (2, 18). At x = 3, y is 31. Plot the point (3, 31). Next, plot points where x is negative. Starting with x = -1. At x = -1, y is 3. Plot the point (-1, 3). At x = -2, y is 6. Plot the point (-2, 6). At x = -3, y = 13. Plot the point (-3, 13). Next, connect the points. As you can see, the graph is somewhat "U" shaped.

    • 4

      Shade in the area of the graph that represents the value of the inequality. Continuing with the example, since y is greater than the equation, the equation represents the area of the graph where y is greater than the lines on the graphs. For this reason, you will shade inside the U where the values of y are greater than the line.

EduJourney © www.0685.com All Rights Reserved