Quadratic Functions and Parabolas

Quadratic Functions and Parabola Characteristics

Vertex Form: y = a(x - h)^2 + k where (h, k) is the vertex point.

Standard Form: y = ax^2 + bx + c.

Converting Forms: use Golden Formula x = -b / (2a) to find the x-value of the vertex.

Axis of Symmetry (AOS): vertical line defined by x = h (vertex x-value).

Minimum or Maximum: minimum or maximum value of function is defined by k (vertex y-value).

Domain: all real numbers.

Range: [k, infinity) if opening upward, or (-infinity, k] if opening downward.