(AOS) axis of symmetry of a parabola
The vertical line that divides a parabola into two symmetric parts. The AOS passes through the vertex.
The axis of symmetry of a parabola is a line that divides the parabola into two equal halves. This line is equidistant from each point on the parabola, and is always perpendicular to the directrix.
The axis of symmetry runs through the vertex of the parabola, which is the point where the parabola changes direction. The vertex is located at the intersection of the axis of symmetry and the parabola itself.
To find the equation of the axis of symmetry, we need to use the vertex form of the equation of a parabola, which is y = a(x – h)^2 + k, where (h,k) is the vertex of the parabola and a is a constant. The axis of symmetry is given by the equation x = h.
For example, if we have the equation y = 2(x – 3)^2 – 4, the vertex of the parabola is (3,-4) and the axis of symmetry is x = 3. This means that any point on the parabola that is equidistant from x = 3 and the directrix will lie on the axis of symmetry.
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