Mathematics ACT Aspire Practice Test 2026 – Complete Study Resource

The quadratic formula is derived from the standard form of a quadratic equation, \( ax² + bx + c = 0 \). It provides a method to find the values of \( x \) that satisfy the equation. The correct formulation is:

\[ x = \frac{-b \pm \sqrt{b² - 4ac}}{2a} \]

This formula includes several crucial components:

1. The expression \(-b\) represents the opposite of the linear coefficient, which helps in finding the correct roots of the equation.

2. The term \(\sqrt{b² - 4ac}\) is known as the discriminant. It determines the nature of the roots: if it is positive, there are two distinct real roots; if zero, there is one real root (a repeated root); and if negative, the roots are complex.

3. The entire fraction is divided by \(2a\), where \(a\) is the leading coefficient of the quadratic term. This division helps to scale the solution appropriately based on the value of \(a\).

The incorrect options either misplace or misrepresent these components, which alters the fundamental basis of what the quadratic formula is supposed to convey. Thus, the correct answer