What is the standard form of a parabola?

The standard form of the equation for a parabola is y = ax^2 + bx + c. A parabola is the set of all points in a plane that are equidistant from a given line and a given point not on the line.

The given point is on the axis of symmetry, which is the vertical line that has exactly half of the parabola on either side; it has the equation x = -b/2a. In the standard form of the equation, "a" determines whether the parabola opens up or down. If a > 0 the parabola opens up, and if a < 0 it opens down. If b = 0, then "c" is the shift of the parabola up or down from the x-axis.