Quadratic Inequalities IES Sierra Nevada Algebra

Quadratics Before we get started let’s review. A quadratic equation is an equation that can be written in the form, where a, b and c are real numbers and a cannot equal zero. In this lesson we are going to discuss quadratic inequalities.

Quadratic Inequalities What do they look like? Here are some examples:

Quadratic Inequalities When solving inequalities we are trying to find all possible values of the variable which will make the inequality true. Consider the inequality We are trying to find all the values of x for which the quadratic is greater than zero.

Solving a quadratic inequality We can find the values where the quadratic equals zero by solving the equation,

Solving a quadratic inequality Now, put these values on a number line and we can see three intervals that we will test in the inequality. We will test one value from each interval.

Solving a quadratic inequality IntervalTest PointEvaluate in the inequalityTrue/False

Solving a quadratic inequality Thus the intervals make up the solution set for the quadratic inequality,. It’s representation is:

Summary In summary, the steps for solving quadratic inequalities are: 1. Solve the equation. 2. Plot the solutions on a number line creating the intervals. 3. Pick a number from each interval and test it in the original inequality. If the result is true, that interval is a solution to the inequality. 4. Write properly the solution (the interval and the representation)

Example 2: Solve First find the zeros by solving the equation, Now consider the intervals around the solutions and test a value from each interval in the inequality.

Example 2: IntervalTest PointEvaluate in InequalityTrue/False

Example 2: Thus the interval makes up the solution set for the inequality. Plot the solution!!

Example 3: Solve the inequality. First find the solutions. WHAT CAN WE DO NOW??

Practice Problems