A parabola's direction refers to the way it opens. Parabolic equations can have two forms: the standard form and the vertex form. Both forms can have either x or y as the input variable. As examples, the standard form with y as an input would be x = a y^2 + b y + c, and the vertex form with x as an input would be y = a * (x  h)^2  k. In both forms, the direction of the parabola's opening is determined by the combination of the acoefficient at the beginning of the equations and the selected input, with an xinput giving a vertical, or up or down, opening and a yinput giving a horizontal, or right or left, opening.
Vertical

Obtain a parabolic equation for an example. With this example, let the equation be y = 6x^2  4x + 10.

Find the acoefficient of the equation. In this example, the acoefficient is 6.

Compare the acoefficient to zero. If the value is greater than zero, the parabola opens upward, and if the value is less than zero, it opens downward. In this example, the acoefficient is 6 and greater than zero, so the parabola opens upward.
Horizontal

Obtain a parabolic equation for example purposes. With this example, let the equation be x = 2 * (y + 2)^2  3.

Find the acoefficient in the equation. In this example, the acoefficient is 2.

Compare the acoefficient to zero. If its value is greater than zero, the parabola opens to the right, and if its value is less than zero, it opens to the left. In this example, the acoefficient of 2 is less than zero, so the parabola opens to the left.