If a quadratic equation is in the form \( ax^2 + bx + c \), what is the axis of symmetry?

The axis of symmetry for a quadratic equation in the standard form ( ax^2 + bx + c ) is derived from the formula that shows where the parabola will be symmetrical about a vertical line. This line, called the axis of symmetry, passes through the vertex of the parabola, which is its highest or lowest point depending on the orientation (opening upwards or downwards).

The formula for the axis of symmetry is given by ( x = -\frac{b}{2a} ). This formula is obtained by finding the vertex of the parabola, which can be calculated by using the values of coefficients ( a ) and ( b ) in the quadratic equation. The negative sign in front of ( b ) indicates the direction necessary to find the vertical line that divides the parabola into two equal halves.

This specific formula tells us that as ( a ) and ( b ) change, the position of the axis of symmetry will adjust accordingly, ensuring the vertex remains at the center of the quadratic function's graph. Thus, the correct choice reflects this mathematical relationship crucial for graphing parabolas effectively.