What is the quadratic formula used to solve for x?

The quadratic formula is derived from the standard form of a quadratic equation, which is expressed as ( ax^2 + bx + c = 0 ). To find the values of ( x ) that satisfy this equation, the quadratic formula provides a direct way to calculate the roots or solutions.

The correct form of the quadratic formula is expressed as ( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} ). In this formula, ( a ), ( b ), and ( c ) represent the coefficients of the quadratic equation. The term ( b^2 - 4ac ) under the square root is known as the discriminant, and it determines the nature of the roots: whether they are real and distinct, real and equal, or complex.

The significance of the negative sign in front of ( b ) is crucial, as it shifts the calculation appropriately based on the position of the vertex of the parabola represented by the quadratic function. The ( \pm ) symbol indicates that there are typically two possible solutions for ( x ), reflecting the symmetrical properties of parabolas about their axis of symmetry.

Understanding the components of the formula helps in solving quadratic