Solve each quadratic inequality. Give the solution set in interval notation. See Example 1. (x - 4)^2 ≤ 0

Key Concepts

Quadratic Inequalities

Quadratic inequalities involve expressions that can be represented in the form ax^2 + bx + c < 0, ax^2 + bx + c > 0, ax^2 + bx + c ≤ 0, or ax^2 + bx + c ≥ 0. To solve these inequalities, one typically finds the roots of the corresponding quadratic equation and then tests intervals to determine where the inequality holds true.

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 (2, 5] includes all numbers greater than 2 and up to 5, including 5 but not 2.

Completing the Square

Completing the square is a method used to transform a quadratic expression into a perfect square trinomial. This technique is particularly useful for solving quadratic equations and inequalities, as it allows for easier identification of roots and the vertex of the parabola. In the context of the given inequality, it helps in determining the values of x that satisfy the condition.