AFOQT Practice Test

Which expression represents the quadratic formula?

1. x = -b ± √(b² + 4ac)/2a

2. x = -b ± √(b² - 4ac)/2a

3. x = b ± √(b² - 4ac)/2a

4. x = -b ± √(b² + 4ac)/2a

The correct answer is: x = -b ± √(b² - 4ac)/2a

The quadratic formula is used to find the solutions (roots) of a quadratic equation, which is typically in the standard form of \( ax^2 + bx + c = 0 \). The correct representation of the quadratic formula is derived from completing the square or using the quadratic formula itself, leading to the roots being expressed as: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] This formula indicates that the discriminant, \( b^2 - 4ac \), determines the nature of the roots of the equation; if it's positive, there are two distinct real roots, if it’s zero, there is one real root, and if it's negative, the roots are complex. The other options present variations that do not conform to the correct formulation. For example, variations in the signs or incorrect usage of the discriminant lead to incorrect representations of the formula. Thus, the option that clearly represents the standard quadratic formula is the one provided.