Vertex Form Quadratics

The vertex form of a quadratic function is f(x) = a(x-h)² + k, where (h, k) is the vertex of the parabola.

The 'a' value indicates the direction of the parabola (upward if a > 0, downward if a < 0) and the width of the parabola (narrower if |a| > 1, wider if |a| < 1).

A positive 'a' value causes the parabola to open upwards.

A negative 'a' value causes the parabola to open downwards.

The expression (x-h) represents a horizontal shift of the graph h units to the right if h is positive and to the left if h is negative.

The '+k' represents a vertical shift of the graph k units up if k is positive and down if k is negative.

The axis of symmetry is the vertical line x = h, where (h, k) is the vertex.

The vertex can be found directly from the vertex form f(x) = a(x-h)² + k as the point (h, k).

A vertical stretch occurs when the absolute value of 'a' is greater than 1, making the parabola narrower.

A vertical shrink occurs when the absolute value of 'a' is less than 1, making the parabola wider.