How to Find the Vertices of Parabolas

A parabola is a mathematical figure of the conical sections category alongside ellipses and hyperbolas. What distinguishes a parabola from the rest of the figures is that all its points are equidistant from a common line of reference known as a directrix. In addition, the points are equidistant from a common point away from the directrix referred to as a focus. A vertex of a parabola simply defines the center point (h, k) of the parabola and is located on the Cartesian plane. The general equation of any given parabola is described as y = ax^2 +bx + c.

Things You'll Need

  • Scientific calculator
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Instructions

    • 1

      Look closely at the equation of the parabola to identify respective values of a and b. For instance, in the equation y = 2x^2 + 6x + 2 the values for "a" would be 2 and "b" would be 6.

    • 2

      Find the result of the multiplication between the value of "b" and -1/2. For this case, the result will give -3.

    • 3

      Perform a division of the result you obtained in Step 2 by the value of "a" in the original equation. In this example, the division will culminate with -1.5 as the answer. In doing this, you now have the x coordinate (h) of the parabola.

    • 4

      Replace the values of the unknown (x) in the original equation by the new obtained value of x to find the value of y coordinate (k). Still on this example, replacing the value of x in the equation gives -2.5. This implies that this figure is the coordinate value of y. Therefore, the vertex (h, k) of the parabola is defined as (-1.5, -2.5).

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