Vertex Form -- Quadratics

The vertex form of a quadratic equation is given by y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

To find the vertex of a parabola in vertex form y = a(x - h)² + k, the vertex is the point (h, k).

The 'a' value indicates the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards.

The standard form of a quadratic equation is y = ax² + bx + c.

To convert from standard form to vertex form, you can complete the square.

The axis of symmetry for a parabola in vertex form y = a(x - h)² + k is the vertical line x = h.

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

If the 'a' value in the vertex form y = a(x - h)² + k is positive, the parabola opens upwards; if negative, it opens downwards.

The vertex (h, k) can be found using h = -b/(2a) and k = f(h), where f(x) is the quadratic function.

The vertex is the midpoint of the roots of the quadratic function, and it lies on the axis of symmetry.