Quadratic Functions

Vertex of a Parabola

A quadratic function is a polynomial function of degree 2, typically written in the form:

• Standard form:

The graph of a quadratic function is a parabola. The vertex of the parabola is its highest or lowest point, depending on the direction it opens.

• If , the parabola opens upward (vertex is a minimum).

• If , the parabola opens downward (vertex is a maximum).

Finding the Vertex

The vertex of the parabola defined by can be found using the formulas:

Thus, the vertex is at .

Example

Given the quadratic function:

Identify , , .

• Calculate :

• Calculate :

Therefore, the vertex is .

• Vertex:

Additional info: The original question asked for the vertex of a quadratic function. The function was interpreted as based on standard notation, as the original text had formatting issues.