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Vertex of a Parabola

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Vertex of a Parabola

In mathematics, the vertex of a parabola is the point on the parabola that is the lowest or highest point, or the point of maximum curvature. A parabola is a curve that is represented by a quadratic equation of the form y = ax^2 + bx + c, where a, b, and c are constants.

You can get the vertex of a parabola by completing the square on the quadratic equation. Completing the square includes adding and subtracting the square of half of the coefficient of the x term (b/2)^2 to the equation so that the equation takes the form (x - h)^2 = k.

The coordinates of the vertex of the parabola are then given by (h, k). For instance, take the parabola y = x^2 + 4x - 3. Completing the square on this equation gives us (x + 2)^2 = 1, so the vertex of the parabola is (-2, 1).

It is necessary to remember that the vertex of a parabola is not constantly the highest or lowest point on the curve. For instance, the vertex of a downward-facing parabola is the highest point on the curve, while the vertex of an upward-facing parabola is the lowest point on the curve.

The vertex of a parabola is a significant point because it is the point where the curve alters direction. It is usually used to define the shape and behavior of the curve.

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