The inherent shape of parabolas gives rise to several characteristics that all quadratic functions have in common. A parabola either opens upward or downward. This is called its direction. Because a parabola either opens upward or downward, there is always one point that is the absolute maximum or absolute minimum of the function. This point is called the vertex.

At the vertex, the function changes from increasing to decreasing, or vice versa.

All parabolas are symmetric, meaning there exists a line that divides the graph into two mirror images. For quadratic functions, that line is always parallel to the $y$-axis, and is called the axis of symmetry.

The axis of symmetry always intersects the vertex of the parabola, and is written as a vertical line, where $h$ can be any real number.

Depending on its rule, a parabola can intersect the $x$-axis at $0,$ $1,$ or $2$ points. Since the function's value at an $x$-intercept is always $0,$ these points are called zeros, or sometimes roots. Because all graphs of quadratic functions extend infinitely to the left and right, they each have a $y$-intercept anywhere along the $y$-axis.