Solve each quadratic inequality. Give the solution set in interval notation. See Exam-ples 5 and 6. x^2≤9

Key Concepts

Quadratic Inequalities

Quadratic inequalities are expressions that involve a quadratic polynomial set in relation to a value, typically using symbols like ≤, ≥, <, or >. To solve these inequalities, one must find the values of the variable that satisfy the inequality, often by determining the roots of the corresponding quadratic equation and analyzing the sign of the quadratic expression in the intervals defined by these roots.

Interval Notation

Interval notation is a mathematical notation used to represent a range of values. It uses parentheses and brackets to indicate whether endpoints are included (closed intervals) or excluded (open intervals). For example, the interval [a, b] includes both a and b, while (a, b) does not. This notation is essential for expressing the solution set of inequalities succinctly.

Graphing Quadratics

Graphing quadratics involves plotting the quadratic function on a coordinate plane to visualize its shape, which is a parabola. The vertex, axis of symmetry, and intercepts are key features that help in understanding the behavior of the quadratic. By graphing the function, one can easily identify the regions where the quadratic is above or below a certain value, aiding in solving inequalities.