Algebra Practice Test 2025 – Complete Exam Preparation

The quadratic formula is specifically designed to find the roots, or solutions, of a quadratic equation of the form \( ax^2 + bx + c = 0 \). This formula is expressed as:

\[

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

\]

Here, \( a \), \( b \), and \( c \) are constants from the quadratic equation, and the term under the square root, \( b^2 - 4ac \), is known as the discriminant. This discriminant indicates not only the existence of real roots but also how many there are: if it's positive, there are two distinct real roots; if it’s zero, there’s exactly one real root (a repeated root); and if it’s negative, the roots are complex and not real.

Using the quadratic formula is particularly effective when the quadratic can’t be easily factored or when one wants to ensure accuracy in finding the roots. It’s an essential tool in algebra for solving various problems requiring the determination of where a quadratic equation crosses the x-axis.

The other options do not relate directly to the main function of the quadratic formula, as they pertain to different algebraic