AFOQT Practice Test

The formula for the axis of symmetry in a quadratic equation is which of the following?

1. x = -b/2a

2. x = -2b/a

3. x = -a/b

4. x = b/2a

The correct answer is: x = -b/2a

The formula for the axis of symmetry in a quadratic equation, which is typically represented in the standard form as \( ax^2 + bx + c = 0 \), is given by the expression \( x = -\frac{b}{2a} \). This formula derives from the vertex form of a quadratic equation, where the axis of symmetry is the vertical line that passes through the vertex of the parabola described by the quadratic equation. The reasoning for this formula is based on the concept that the quadratic function is symmetric about its vertex. When calculating the vertex, the x-coordinate is found by taking the derivative of the function and setting it to zero, leading to the same formula. The term \( -\frac{b}{2a} \) provides the x-value where the maximum or minimum of the parabola occurs, marking the point of symmetry. Therefore, if the vertex is known, one can reflect points across this line to find equal distances on either side of the parabola. This understanding of parabolas and their properties reinforces why this particular formula is used to describe the axis of symmetry effectively.