How to Find the Vertex of a Quadratic Function
Finding the vertex of a quadratic function is essential for graphing and understanding its properties. A quadratic function is generally expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants. The vertex represents the highest or lowest point of the parabola, depending on the value of a.
Method 1: Using the Vertex Formula
The vertex can be found using the formula: x = -b / (2a). Once you have the x-coordinate, substitute it back into the original equation to find the y-coordinate. Therefore, the vertex coordinates are (-b / (2a), f(-b / (2a))).
Method 2: Completing the Square
Another method to find the vertex is by completing the square. Start with the standard form of the quadratic equation and rearrange it to obtain the vertex form f(x) = a(x - h)² + k, where (h, k) is the vertex. This method provides a clear visual representation of the vertex.
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