Definition: The axis of symmetry of a parabola is the vertical line through its vertex that divides the graph into two mirror-image halves.
What is the axis of symmetry?
If you fold the graph along this line, the two sides match exactly. For a parabola y = ax2 + bx + c, the line is x = -b / (2a). It is the same x-value as the vertex.
How do you use it?
Points on the parabola come in mirror pairs at equal distance from the axis. If you know one point, you can find its twin without extra calculation. The midpoint of the two zeros also lies on the axis.
Example. The parabola y = x2 – 10x + 16 has axis x = 5. The point (1, 7) is 4 units left of the axis, so (9, 7) is on the graph too. The zeros are 2 and 8; their average is 5, which matches the axis.
What should you avoid?
Writing the axis as a point or as y = something. It is a vertical line, so it must be written as x = a number. Another slip is to drop the negative sign in the formula, which moves the axis to the wrong side of the y-axis.