Ohio Assessments for Educators (OAE) Mathematics Practice Exam

Which formula is used to find the axis of symmetry of a parabola given by ax² + bx + c?

1. -b/2a

2. b/2a

3. -2b/a

4. 2b/a

The correct answer is: -b/2a

The correct formula to find the axis of symmetry for a parabola defined by the quadratic equation \( ax^2 + bx + c \) is \( -\frac{b}{2a} \). This is derived from the standard form of the quadratic function and represents the vertical line that divides the parabola into two mirror-image halves. The axis of symmetry is crucial because it tells you where the highest or lowest point of the parabola, known as the vertex, is located. The vertex occurs at the x-value given by this formula. When you substitute values into the formula, you are effectively finding the x-coordinate of the vertex, which allows you to understand the shape and direction of the parabola. In this context, the other formulas presented do not yield the correct relationship for determining the axis of symmetry. For instance, \( \frac{b}{2a} \) would provide an incorrect value, and the options involving \( -2b/a \) and \( 2b/a \) also do not align with the established quadratic principles that govern parabolic equations. Thus, it's crucial to remember that the axis of symmetry can be directly calculated using \( -\frac{b}{2a} \), providing a reliable method