Understanding the Vertex of a Parabola | Key Concepts and Calculation Steps

vertex of a parabola

In mathematics, a parabola is a symmetric curve that can be represented by a quadratic equation of the form y = ax^2 + bx + c, where a, b, and c are constants

In mathematics, a parabola is a symmetric curve that can be represented by a quadratic equation of the form y = ax^2 + bx + c, where a, b, and c are constants. The vertex of a parabola is a crucial point on the curve that represents the minimum or maximum value of the quadratic function.

The vertex is the point where the parabola reaches its extreme value along the vertical axis. If the parabola opens upwards, the vertex will be the lowest point on the curve, known as the minimum point. Conversely, if the parabola opens downwards, the vertex will be the highest point on the curve, called the maximum point.

To find the coordinates of the vertex, you can follow these steps:

1. Identify the coefficients a, b, and c from the quadratic equation.
2. Use the formula x = -b / (2a) to find the x-coordinate of the vertex. This formula represents the axis of symmetry of the parabola.
3. Substitute the x-coordinate found in step 2 back into the original equation to calculate the y-coordinate of the vertex.

Once you have the x and y coordinates of the vertex, the vertex can be represented as (x, y). The vertex not only provides information about the extreme points of the parabola but also determines the direction in which the parabola opens.

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