Which of the following represents the quadratic formula?

The quadratic formula is derived from the standard form of a quadratic equation, which is written as ( ax^2 + bx + c = 0 ). To solve for ( x ) in this equation, one of the methods involves completing the square, which ultimately leads us to the formula:

[

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

]

In this expression, ( -b ) represents the negation of the coefficient of the linear term, while the discriminant ( b^2 - 4ac ) determines the nature of the roots. The term ( \sqrt{b^2 - 4ac} ) indicates that we're considering both potential solutions, hence the ( \pm ) symbol. Finally, all of this is divided by ( 2a ), which reflects the scaling factor related to the leading coefficient of the quadratic equation.

The correct choice accurately depicts this setup, specifically ensuring that all terms are placed correctly within the formula’s structure. Each component of the formula directly corresponds to its role in solving the quadratic equation, making the answer a precise representation of the quadratic formula as recognized in algebra.