What is the quadratic formula used for?

The quadratic formula is specifically designed to find the roots of quadratic equations, which are polynomial equations of the form ax^2 + bx + c = 0, where a, b, and c are constants, and a is not equal to zero. The formula, expressed as x = [-b ± √(b² - 4ac)] / (2a), allows for the calculation of the values of x that satisfy this equation. In essence, it provides a systematic method to determine the x-values where the parabola intersects the x-axis.

The roots found using the quadratic formula can be real or complex, depending on the value of the discriminant (b² - 4ac). If the discriminant is positive, there are two distinct real roots; if it is zero, there is one real root (a repeated root); and if it is negative, there are two complex roots. Understanding this formula is crucial for solving various problems in algebra that pertain to the behavior of quadratic functions.