axis of symmetry

The axis of symmetry is the invisible vertical line that splits a parabola into two mirror-image halves. If you placed a mirror along this line, each side of the curve would reflect onto the other perfectly. It always runs straight up and down, passing right through the vertex.

For a parabola from f(x) = ax^2 + bx + c, the axis of symmetry is the line x = -b/(2a). Notice this is the same as the x-coordinate of the vertex — the axis and the vertex share that value, because the axis is precisely the line through the turning point.

This symmetry is a handy shortcut. Any two inputs that are equally far from the axis give the same output. So if you know the parabola passes through (1, 7) and the axis is x = 4, it must also pass through (7, 7) — the mirror image three units to the other side.