Vertex and Axis of Symmetry
The axis of symmetry is the turning point of a quadratic function. If the graph opens up (i.e., a>0), then the vertex is the lowest point on the graph; if it opens down (i.e., a<0) then the vertex is the highest point on the graph. The line of symmetry is the vertical line that passes through the vertex point. Each point on the right side of the parabola has a mirror-image (horizontally) on the left side. This means that their horizontal distance from the axis of symmetry is always the same.
The sliders h and v move the curve either horizontally (left or right), or vertically (up or down). Note that the line of symmetry "follows" the curve when it is moved horizontally, but stays in place when it is moved vertically. The slider s traces a point on the axis of symmetry. Note that the horizontal distance from this point to the right side of the curve (with respect to the axis of symmetry) is always equal to the corresponding point on the left side of the curve.