The expression used to calculate the discriminant of a quadratic equation of the form \( ax^2 + bx + c = 0 \) is given by:
\[ D = b^2 - 4ac \]
where \( D \) represents the discriminant. This discriminant is critical for determining the nature of the roots of the quadratic equation.
So, the correct answer from the options provided is:
\[ b^2 - 4ac \]