Which expression represents the quadratic formula?

The quadratic formula is derived from the general form of a quadratic equation, which is written as ( ax^2 + bx + c = 0 ). The formula is used to find the values of ( x ) that satisfy this equation.

The correct expression, which is represented by the first choice, ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ), is derived through the process of completing the square. The term ( b^2 - 4ac ) is known as the discriminant, and it determines the nature of the roots of the quadratic equation. Specifically, it indicates whether the roots are real and distinct, real and equal, or complex.

In summary, this option correctly captures the necessary components of the quadratic formula, allowing for the accurate determination of the roots of any quadratic equation when given values for ( a ), ( b ), and ( c ). The other expressions contain errors related to the signs, the constants, or the discriminant part that do not conform to the standard form of the quadratic formula.