Which of the following represents the quadratic formula?

The quadratic formula is used to find the solutions (roots) of a quadratic equation, which generally takes the form ax² + bx + c = 0, where a, b, and c are constants and a is not zero. The correct representation of the quadratic formula is derived from the process of completing the square.

In the formula, x = (-b ± √(b² - 4ac)) / 2a, the term -b represents the negation of the coefficient of x, while the square root component √(b² - 4ac) relates to the discriminant, which indicates the nature of the roots (real and distinct, real and equal, or complex). Dividing by 2a normalizes the solution according to the leading coefficient of the quadratic term.

This formula encapsulates both possible solutions for x (due to the ± symbol), providing a comprehensive method for solving any quadratic equation. The other options do not represent the quadratic formula and serve different mathematical purposes. For instance, one pertains to the vertex of a parabola, while others simplify to means or geometric interpretations that do not relate to solving quadratic equations.