Quadratic Functions and Their Graphs

Vertex of a Parabola

The vertex of a quadratic function is the highest or lowest point on its graph, depending on whether the parabola opens upward or downward. For a function in the form f(x) = ax^2 + bx + c, the vertex can be found using a specific formula.

• Standard Form:

• Vertex Formula: The x-coordinate of the vertex is

• To find the y-coordinate, substitute this x-value back into the function:

Example: Find the Vertex of

• Identify coefficients: , ,

• Find x-coordinate:

• Find y-coordinate: Substitute into the function:

• Vertex:

Summary Table: Vertex of a Quadratic Function

• Application: The vertex represents the minimum point of the parabola since (the parabola opens upward).