Unit 3: Quadratic Inequalities - Solving Quadratic Inequalities in One Variable

Vocabulary flashcards covering key definitions and notation rules for solving quadratic inequalities in one variable.

Quadratic Inequality

An inequality with one unknown of degree 2 that follows one of the standard forms: $ax^2 + bx + c < 0$, $ax^2 + bx + c > 0$, $ax^2 + bx + c \ge 0$, or $ax^2 + bx + c \le 0$.

Critical Numbers

The solutions of the equivalent quadratic equation of a given quadratic inequality.

Test Intervals

The intervals into which the critical numbers divide the real number line.

Test Numbers

Values of $x$ taken from each test interval and substituted into the quadratic inequality to determine whether the interval satisfies the inequality.

Parentheses in Interval Notation

Notation used in interval notation when critical numbers are not part of the solution set, corresponding to the inequality symbols $<$ or $>$.

Brackets in Interval Notation

Notation used in interval notation when critical numbers are included in the solution set, corresponding to the inequality symbols $\le$ or $\ge$.

Hollow Points on a Number Line

Open circles plotted on a number line showing that the critical numbers are not included in the solution set.