A quadratic inequality is an inequality that contains a quadratic function, with the highest degree of the variable being 2. It can be written in the form of ax^2 + bx + c < 0, where a, b, and c are constants and x is the variable.
Interval notation is a way of representing the solution set of an inequality using a combination of parentheses and brackets. For example, (a, b) would represent all real numbers between a and b, including a and b, while [a, b] would represent all real numbers between a and b, including a but not b.
To graph a quadratic inequality, first plot the corresponding quadratic function. Then, determine whether the inequality is less than or greater than, and shade the appropriate region on the graph. If the inequality includes an equal sign, use a solid line for the boundary. If the inequality does not include an equal sign, use a dashed line for the boundary.
The solution set of a quadratic inequality is the set of all real numbers that make the inequality true. It can be represented using interval notation or set-builder notation.
Quadratic inequalities can be used to model and solve real-world problems, such as determining the maximum or minimum value of a function, optimizing a business's profits, or finding the range of possible values for a given situation.