What is the quadratic formula used to find the roots of a quadratic equation?

The quadratic formula is a fundamental tool in algebra for finding the roots (solutions) of a quadratic equation in the form ( ax^2 + bx + c = 0 ). The correct formula, represented accurately, is:

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

In this formula, "b" is the coefficient of the linear term, "a" is the coefficient of the quadratic term, and "c" is the constant term. The expression under the square root, ( b^2 - 4ac ), is known as the discriminant and determines the nature of the roots of the quadratic equation.

Choosing the correct formula is critical because it ensures that you can accurately calculate the values of ( x ) where the parabola intersects the x-axis. The use of the negative sign in front of "b" is significant for flipping the sign of "b" in the formula, leading to correct solutions when considering both (\pm), which accounts for the two possible roots of the equation.

The alternatives presented do not include the necessary negative sign before "b" or misapply the terms, which would result in incorrect or nonsensical