Vertex form

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

The vertex can be identified as the point (h, k) in the vertex form $$y = a(x-h)^2 + k$$ .

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

The term $$k$$ represents a vertical shift of the graph up by k units if k is positive and down if k is negative.

If the parabola opens upwards, it means that the 'a' value in the vertex form is positive, indicating a minimum point at the vertex.

If the parabola opens downwards, it means that the 'a' value in the vertex form is negative, indicating a maximum point at the vertex.

A parabola is narrow if |a| > 1 and wide if |a| < 1 in the vertex form $$y = a(x-h)^2 + k$$ .

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

The graph shifts left 2 units and down 3 units.