Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the formula for solving a quadratic equation?

1. -b ± √(b² - 4ac) / (2a)

2. ax² + bx + c = 0

3. x = (-b ± √(b² + 4ac)) / (2a)

4. b² - 4ac = 0

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

The formula for solving a quadratic equation is given by the quadratic formula, which is expressed as x = (-b ± √(b² - 4ac)) / (2a). This formula allows you to find the roots of any quadratic equation of the standard form ax² + bx + c = 0, where a, b, and c are constants, and 'a' is not equal to zero. In this formula, 'b' represents the coefficient of the linear term, and 'a' is the coefficient of the quadratic term. The term under the square root, b² - 4ac, 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 ± symbol indicates that there are generally two solutions for x, which corresponds to the two potential points at which the parabola intersects the x-axis. Other options provided include variations and components related to quadratic equations but do not represent the complete and correct formula for finding the solutions. For example, one option lists the standard form of the equation itself, while another contains an incorrect sign in the discriminant. The fourth option represents the condition for the roots being equal (when the discrimin