Quadratic Inequalities - Examples, Exercises and Solutions

The quadratic inequality shows us in which interval the function is positive and in which it is negative - according to the inequality symbol. To solve quadratic inequalities correctly, it is convenient to remember two things:

1. Set of positivity and negativity of the function:
   Set of positivity - represents the $X$s in which the graph of the parabola is above the $X$ axis, with $Y$ value positive.
   Set of negativity - represents the $X$s in which the graph of the parabola is below the $X$ axis, with $Y$ value negative.
2. Dividing by a negative term - reverses the sign of the inequality.

Method to solve the quadratic inequality:

1. We will carry out the transposition of members and isolate the quadratic equation until one side equals 0. Remember that when we divide by a negative term, the inequality is reversed.
2. Let's draw a diagram of the parabola - placing points of intersection with the $X$ axis and identifying the maximum and minimum of the parabola.
3. Let's calculate the corresponding interval according to the exercise and the diagram.
   Quadratic equation $>0∶$ Set of positivity
   Quadratic equation $<0∶$ Set of negativity