A quadratic inequality is a mathematical expression that involves a quadratic function, typically in the form of ax^2 + bx + c , where a , b , and c are constants. Unlike a quadratic equation, which sets the expression equal to zero, a quadratic inequality uses symbols like < , > , \leq , or \geq to describe a range of values for x that satisfy the condition. To solve a quadratic inequality, one usually starts by finding the roots of the corresponding quadratic equation ax^2 + bx + c = 0 . These roots divide the number line into intervals. By testing points from each interval, one can determine where the inequality holds true. The solution is often expressed in interval notation, indicating the values of x that satisfy the inequality, which can be visualized on a graph involving the parabola represented by the quadratic function.