What is the axis of symmetry of a graph?

• A. A line that divides a graph into two congruent reflected halves
• B. A line that passes through the origin
• C. The slope of a parabola at its vertex
• D. A vertical line always at x=0

Answer: (A)

The axis of symmetry is a line along which the graph can be folded so that the two sides line up exactly as mirror images. In other words, every point on one side has a corresponding reflected point on the other side across that line. For many parabolas, the axis is a vertical line that goes through the vertex (for a parabola in standard position, x = h if the vertex is at (h, k)). It doesn’t have to pass through the origin, and it isn’t determined by the slope at the vertex. A line x = 0 is just a special case when the vertex happens to lie on that line.