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.

The value of 'a' determines the direction and width of the parabola. If 'a' is positive, the parabola opens upwards; if 'a' is negative, it opens downwards. A larger absolute value of 'a' results in a narrower parabola.

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

In the vertex form $$y = a(x - h)^2 + k$$ , the vertex is the point (h, k).

This equation represents a translation of the basic parabola $$y = x^2$$ , shifted left 2 units and down 3 units.

The axis of symmetry is the vertical line $$x = 4$$ .

To convert from standard form $$y = ax^2 + bx + c$$ to vertex form, complete the square.

A negative 'a' value reflects the parabola over the x-axis.

If a parabola opens upwards, its vertex is the minimum point on the graph.

The vertex is (-1, 5).