What is the equation for the axis of symmetry in a quadratic function?

The equation for the axis of symmetry in a quadratic function is derived from the standard form of a quadratic equation, which is typically expressed as (y = ax^2 + bx + c). The axis of symmetry can be found using the formula (x = -\frac{b}{2a}). This formula essentially provides the x-coordinate of the vertex of the parabola represented by the quadratic function.

To understand this formula, consider that a parabola is symmetric with respect to a vertical line that passes through its vertex. This line is the axis of symmetry, and its position is determined by the coefficients (a) and (b) in the equation.

The coefficient (b) represents the linear term's influence, while (a) is associated with the curvature of the parabola (whether it opens upwards or downwards). Thus, the formula effectively balances the contributions of these coefficients to find the precise point where the parabola is symmetric.

The correct choice clearly reflects this relationship, indicating that the axis of symmetry is directly related to both (b) (the coefficient of (x)) and (a) (the coefficient of (x^2)). By understanding this derivation, one can effectively