Which expression represents the standard form of a quadratic equation?

Which expression represents the standard form of a quadratic equation?

• A. a x^2 + b x - c = 0
• B. ax^2 + bx + c = 0
• C. x^2 + bx + c = 0
• D. a^2 x^2 + b x + c = 0

Answer: (B)

The standard form of a quadratic equation expresses the equation with a nonzero coefficient in front of x^2, followed by the linear term and then the constant, all set equal to zero. The pattern is a x^2 + b x + c = 0, where a, b, and c are constants and a ≠ 0. This arrangement shows the leading quadratic term clearly and identifies the coefficients that shape the parabola. The expression that fits this description has the leading coefficient a in front of x^2, the linear term bx, and the constant c, with the right-hand side equal to zero. The other options alter the sign of the constant, omit the leading a, or place a^2 in front of x^2, which aren’t part of the standard form.

The standard form of a quadratic equation expresses the equation with a nonzero coefficient in front of x^2, followed by the linear term and then the constant, all set equal to zero. The pattern is a x^2 + b x + c = 0, where a, b, and c are constants and a ≠ 0. This arrangement shows the leading quadratic term clearly and identifies the coefficients that shape the parabola.

The expression that fits this description has the leading coefficient a in front of x^2, the linear term bx, and the constant c, with the right-hand side equal to zero. The other options alter the sign of the constant, omit the leading a, or place a^2 in front of x^2, which aren’t part of the standard form.