How do you find the vertex of a quadratic function and determine if it represents a maximum or minimum point?

To find the vertex of a quadratic function in the form y = ax^2 + bx + c, use the formula x = -b/(2a). Substitute this x-value back into the function to find the y-coordinate. If a > 0, the vertex is a minimum point; if a < 0, it is a maximum point.