How to Find the Coordinates of a Vertex in Vertex Form

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Finding a parabola's vertex sometimes requires no graphing and no math. Parabolas are expressed algebraically in quadratic equations, also termed parabolic. The two forms of parabolic equations are the standard and the vertex form. The vertex form is given as y = a * (x - h)^2 + k, in which x and y are variables and a, h and k are coefficients, and is named so because it actually gives the vertex's Cartesian coordinates in the equation. You can find the vertex's coordinates from the vertex form by knowing where to look.

  • Obtain the equation of a parabola in vertex form for example purposes. For an example, let the equation be y = (x + 4)^2 - 10.

  • Find the h-coefficient's value, and change its sign to calculate the vertex's x-coordinate. In this example, the value of h is 4, a positive number. Changing the number's sign to negative results in -4.

  • Find the k-coefficient's value to calculate the vertex's y-coordinate. Concluding this example, the value of k is -10. The parabola's vertex has the coordinates (-4,-10).

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