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.

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

The 'h' value represents the x-coordinate of the vertex and indicates horizontal shifts of the parabola.

The 'k' value represents the y-coordinate of the vertex and indicates vertical shifts of the parabola.

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

The axis of symmetry can be found using the formula $$x = h$$ , where 'h' is the x-coordinate of the vertex.

This equation represents a reflection over the x-axis, a vertical stretch by a factor of 3, a left shift of 2 units, and an upward shift of 4 units.

A negative 'a' value indicates that the parabola opens downwards, meaning it has a maximum point.

The maximum or minimum value is given by the y-coordinate of the vertex (k). If 'a' is positive, it's a minimum; if 'a' is negative, it's a maximum.

Changing the 'a' value affects the width and direction of the parabola. A larger absolute value of 'a' makes the parabola narrower, while a smaller absolute value makes it wider.